Concept explainers
Determine the kinetic energy of the 100-kg object.
a)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the disk is
Explanation of Solution
Given:
The mass of disk is
The angular velocity of the disk is
The radius of the disk is
Draw the free body diagram of the rod as shown in Figure (1a).
Refer Figure (1a).
Write the formula for mass moment of inertia
Here,
Write the formula for kinetic energy
(Rotation about fixed axis).
Substitute
Here,
Conclusion:
Calculate the kinetic energy of the disk.
Substitute
Thus, the kinetic energy of the disk is
b)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the disk is
Explanation of Solution
Given:
The mass of rod is
The angular velocity of the rod is
The length of the rod is
Draw the free body diagram of the rod as shown in Figure (1b).
Refer Figure (1b).
Write the formula for mass moment of inertia
Here,
Substitute
Here,
Write the formula for kinetic energy
Substitute
Here,
Conclusion:
Refer Figure (1b).
Calculate the kinetic energy of the rod.
Substitute
Thus, the kinetic energy of the rod is
c)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the disk is
Explanation of Solution
Given:
The mass of disk is
The angular velocity of the disk is
The radius of the disk is
Draw the free body diagram of the disk as shown in Figure (1c).
Refer Figure (1c).
Write the formula for mass moment of inertia
Here,
Write the formula for kinetic energy
Here,
Substitute
Here,
Conclusion:
Refer Figure (1c).
Calculate the kinetic energy of the disk.
Substitute
Thus, the kinetic energy of the disk is
d)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the rod is
Explanation of Solution
Given:
The mass of rod is
The angular velocity of the rod is
The length of the rod is
Draw the free body diagram of the rod as shown in Figure (1d).
Refer Figure (1d).
Write the formula for mass moment of inertia
Here,
Write the formula for kinetic energy
(Rotation about fixed axis).
Substitute
Here,
Conclusion:
Refer Figure (1d).
Calculate the kinetic energy of the rod.
Substitute
Thus, the kinetic energy of the rod is
e)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the disk is
Explanation of Solution
Given:
The mass of disk is
The angular velocity of the disk is
The radius of the disk is
Draw the free body diagram of the disk as shown in Figure (1e).
Refer Figure (1e).
Write the formula for mass moment of inertia
Here,
Write the formula for kinetic energy
Here,
Substitute
Here,
Conclusion:
Refer Figure (1e).
Calculate the kinetic energy of the disk.
Substitute
Thus, the kinetic energy of the disk is
f)
The kinetic energy of the object:
Answer to Problem 1PP
The kinetic energy of the disk is
Explanation of Solution
Given:
The mass of rod is
The angular velocity is
Draw the free body diagram of the object as shown in Figure (1f).
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
Write the formula for kinetic energy
(Rotation about fixed axis).
Here,
Substitute
Here,
Conclusion:
Refer Figure (1f).
Here
Calculate the kinetic energy of the disk.
Substitute
Thus, the kinetic energy of the disk is
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Chapter 18 Solutions
Engineering Mechanics: Dynamics, Study Pack, Si Edition
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