Determine the kinetic energy of the 100-kg object.

Question

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Answer 1

Textbook Question

Chapter 18.4, Problem 1PP

Determine the kinetic energy of the 100-kg object.

Chapter 18.4, Problem 1PP, Determine the kinetic energy of the 100-kg object.

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

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Answer 2

Textbook Question

Chapter 18.4, Problem 1PP

Determine the kinetic energy of the 100-kg object.

Chapter 18.4, Problem 1PP, Determine the kinetic energy of the 100-kg object.

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 18.4, Problem 1PP

Determine the kinetic energy of the 100-kg object.

Chapter 18.4, Problem 1PP, Determine the kinetic energy of the 100-kg object.

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

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Answer 4

Textbook Question

Chapter 18.4, Problem 1PP

Determine the kinetic energy of the 100-kg object.

Chapter 18.4, Problem 1PP, Determine the kinetic energy of the 100-kg object.

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

Answer 8

a)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The kinetic energy of the object:

Answer 13

Answer to Problem 1PP

The kinetic energy of the disk is $900 J$ .

Answer 14

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the rod as shown in Figure (1a).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 1

Refer Figure (1a).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12Iω2$

Substitute $12mr2$ for $I$ .

$T=12(12mr2)ω$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=12[12(100 kg)(2 m)2](3 rad/s)2=12(200)(9)=900 J$

Thus, the kinetic energy of the disk is $900 J$ .

Answer 15

b)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The kinetic energy of the object:

Answer 20

Answer to Problem 1PP

The kinetic energy of the disk is $800 J$ .

Answer 21

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $6 m$ .

Draw the free body diagram of the rod as shown in Figure (1b).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 2

Refer Figure (1b).

Write the formula for mass moment of inertia $(IO)$ of the rod about the point $O$ .

$IO=IG+mlOG2$ (I)

Here, $IG$ is the moment of inertial about the centroid $G$ and $IG=112ml2$ .

Substitute $112ml2$ for $IG$ in Equation (I).

$IO=112ml2+mlOG2$

Here, $IO$ is the mass moment of inertia about point $O$ , $m$ is the mass, $l$ is the total length of the rod and $lOG$ , distance between the point $O and G$ .

Write the formula for kinetic energy $(T)$ .

$T=12IOω2$

Substitute $112ml2+mlOG2$ for $IO$ .

$T=12(112ml2+mlOG2)ω2$ (I)

Here, $ω$ is the angular velocity.

Conclusion:

Refer Figure (1b).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $6 m$ for $l$ , $1 m$ for $lOG$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[112(100 kg)(6 m)2+(100 kg)(1 m)2](2 rad/s)2=12(400)(4)=800 J$

Thus, the kinetic energy of the rod is $800 J$ .

Answer 22

c)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

The kinetic energy of the object:

Answer 27

Answer to Problem 1PP

The kinetic energy of the disk is $1200 J$ .

Answer 28

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=3 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1c).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 3

Refer Figure (1c).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1c).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $3 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×2 rad/s)2]+12[12(100 kg)(2 m)2](2 rad/s)2=800+400=1200 J$

Thus, the kinetic energy of the disk is $1200 J$ .

Answer 29

d)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

Answer 30

d)

Expert Solution

Answer 31

d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

The kinetic energy of the object:

Answer 34

Answer to Problem 1PP

The kinetic energy of the rod is $600 J$ .

Answer 35

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity of the rod is $ω=2 rad/s$ .

The length of the rod is $3 m$ .

Draw the free body diagram of the rod as shown in Figure (1d).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 4

Refer Figure (1d).

Write the formula for mass moment of inertia $(IO)$ of the rod having the rotation axis at one end.

$IO=13ml2$

Here, $m$ is the mass and $l$ is the length of the rod about mass center O.

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12IOω2$

Substitute $13ml2$ for $IO$ .

$T=12(13ml2)ω2$ (I)

Here, $IO$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1d).

Calculate the kinetic energy of the rod.

Substitute $100 kg$ for $m$ , $3 m$ for $l$ and $2 rad/s$ for $ω$ in Equation (I).

$T=12[13(100 kg)(3 m)2](2 rad/s)2=12(300)(4)=600 J$

Thus, the kinetic energy of the rod is $600 J$ .

Answer 36

e)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

Answer 37

e)

Expert Solution

Answer 38

e)

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

The kinetic energy of the object:

Answer 41

Answer to Problem 1PP

The kinetic energy of the disk is $4800 J$ .

Answer 42

Explanation of Solution

Given:

The mass of disk is $100 kg$ .

The angular velocity of the disk is $ω=4 rad/s$ .

The radius of the disk is $2 m$ .

Draw the free body diagram of the disk as shown in Figure (1e).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 5

Refer Figure (1e).

Write the formula for mass moment of inertia $(I)$ of the disk about it is center.

$I=12mr2$

Here, $m$ is the mass and $r$ is the radius of the disk.

Write the formula for kinetic energy $(T)$ .

$T=12mv2+12Iω2$

Here, $v=rω$ .

Substitute $rω$ for $v$ and $12mr2$ for $I$ .

$T=12m(rω)2+12(12mr2)ω2$ (I)

Here, $m$ is the mass, $r$ is radius, $I$ is the mass moment of inertia and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1e).

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=[12(100 kg)(2 m×4 rad/s)2]+12[12(100 kg)(2 m)2](4 rad/s)2=3200+1600=4800 J$

Thus, the kinetic energy of the disk is $4800 J$ .

Answer 43

f)

Expert Solution

To determine

The kinetic energy of the object:

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

Answer 44

f)

Expert Solution

Answer 45

f)

Expert Solution

Answer 46

Expert Solution

Answer 47

To determine

The kinetic energy of the object:

Answer 48

Answer to Problem 1PP

The kinetic energy of the disk is $3200 J$ .

Answer 49

Explanation of Solution

Given:

The mass of rod is $100 kg$ .

The angular velocity is $ω=4 rad/s$ .

Draw the free body diagram of the object as shown in Figure (1f).

ENGINEERING MECH DYNAMICS W/MASTREV, Chapter 18.4, Problem 1PP , additional homework tip 6

Refer Figure (1f).

Here, the ends of the rod are connected to two rods of same length. Hence the rod travels in circular motion.

Consider as the mass travels in a radius of $r=2 m$ .

Write the formula for kinetic energy $(T)$

(Rotation about fixed axis).

$T=12mv2$

Here, $v=rω$ .

Substitute $rω$ for $v$ .

$T=12m(rω)2$ (I)

Here, $m$ is the mass, $r$ is radius and $ω$ is the angular velocity.

Conclusion:

Refer Figure (1f).

Here $r=2 m$ .

Calculate the kinetic energy of the disk.

Substitute $100 kg$ for $m$ , $2 m$ for $r$ and $4 rad/s$ for $ω$ in Equation (I).

$T=12(100 kg)[(4 rad/s)(2 m)]2=50(64)=3200 J$

Thus, the kinetic energy of the disk is $3200 J$ .

Answer 50

Ch. 18.4 - Determine the kinetic energy of the 100-kg object.Ch. 18.4 - The 80-kg wheel has a radius of gyration about its...Ch. 18.4 - If the rod is at rest when = 0, determine its...Ch. 18.4 - Determine the angular velocity of the rod when the...Ch. 18.4 - If the wheel starts from rest and rolls Without...Ch. 18.4 - If the uniform 30-kg slender rod starts from rest...Ch. 18.4 - When it is subjected to a couple moment of M = 50...Ch. 18.4 - Show that its kinetic energy can be represented a...Ch. 18.4 - If the torsional spring attached to the wheel's...Ch. 18.4 - If the torsional spring attached to the wheel's...

Determine the kinetic energy of the 100-kg object.

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