Engineering Mechanics: Dynamics (14th Edition)
Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 14.3, Problem 1PP

Determine the work of the force when it displaces 2 m.

Chapter 14.3, Problem 1PP, Determine the work of the force when it displaces 2 m. , example  1

Chapter 14.3, Problem 1PP, Determine the work of the force when it displaces 2 m. , example  2

a)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is 600J .

Explanation of Solution

Given:

The force acting on the block is F=500N .

The displacement of the block is s=2m .

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  1

Write the formula for work done force (F) .

UF=Fs (I)

Here, F is the force and s is the displacement of the block.

Conclusion:

Refer Figure (a).

Resolve the force along xaxis .

F=500N(35)=300N

Substitute 300N for F and 2m for s in Equation (I).

UF=300N(2m)=600Nm×1J1Nm= 600J

Thus, the work done by the force on the block is 600J .

b)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is 0J .

Explanation of Solution

Given:

The force acting on the block is F=98.1N .

The displacement of the block is s=2m .

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  2

Write the formula for work done force (F) .

UF=Fs (I)

Here, F is the force and s is the displacement of the block.

Conclusion:

Refer Figure (1).

The force acting on the block does not cause any displacement of the block. Hence the work done by the force is zero.

Thus, the work done by the force on the block is 0J .

c)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is 16J .

Explanation of Solution

Given:

The force acting on the block is F=(6s2)N .

The displacement of the block is s=2m .

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  3

Write the formula for work done force (F) .

UF=s1s2Fds (I)

Here, F is the force and s1,s2 is the initial and final displacement of the block.

Conclusion:

Refer Figure (c).

Substitute 6s2 for F , 0 for s1 and 2m for s2 in Equation (I).

UF=026s2ds=6[s33]02=2(2303)=16J

Thus, the work done by the force on the block is 16J .

d)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is  120J .

Explanation of Solution

Given:

The force acting on the block is F=500N .

The displacement of the block is s=2m .

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  4

Write the formula for work done force (F) .

UF=Fs (I)

Here, F is the force and s is the displacement of the block.

Conclusion:

Refer Figure (d).

Resolve the force along xaxis .

F=100N(35)=60N

Substitute 60N for F and 2m for s in Equation (I).

UF=60N(2m)=120Nm×1J1Nm= 120J

Thus, the work done by the force on the block is  120J .

e)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is 24J .

Explanation of Solution

Given:

The displacement of the block is s=2m .

The given Fs graph is shown in Figure (e).

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  5

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  6

The graph consists of two geometrical cross sectional areas namely triangle and rectangle.

Write the formula for work done force (F) .

UF=Area under the Fsgraph ×45=(Ar+At)×45 (I)

Here, F is the force and s is the displacement of the block.

Refer Figure (e).

Write the formula for triangle.

At=12b1h (II)

Write the formula for rectangle.

Ar=b2h (III)

Conclusion:

Refer Figure (e).

Calculate the area under the Fs graph.

Substitute 1m for b1 and 20N for h in Equation (II).

At=12(1m)(20N)=10Nm

Substitute 1m for b2 and 20N for h in Equation (III).

Ar=(1m)(20N)=20Nm

Calculate the work done by the force (F) .

Substitute 10Nm for At and 20Nm for Ar in Equation (I).

UF=(10Nm+20Nm)×45=30×45=24Nm×1J1Nm=24J

Thus, the work done by the force on the block is 24J .

f)

Expert Solution
Check Mark
To determine

The work of a spring force.

Answer to Problem 1PP

The work done by the force on the block is 40J .

Explanation of Solution

Given:

The stiffness of the spring is 10N/m .

The spring is originally compressed to 3m .

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

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  7

Write the formula for work done force (Fsp) .

UFsp=12k(s02s12) (I)

Here, k is the stiffness of the spring, s0 is the unstretched length of the spring and s1 is the final displacement of the spring.

Conclusion:

Refer Figure (f).

Here, the block is subjected to spring force only.

When the spring is originally compressed to 3m , the unstretched length of the spring is

s0=3m .

When the spring is released, the displaced to 2m . Hence the final displacement of the spring is s1=3m2m=1m .

Substitute 10N/m for k , 3m for s0 and 1m for s1 in Equation (I).

Usp=12×10N/m[(3m)2(1m)2]=5×8= 40J

Thus, the work done by the spring force on the block is 40J .

g)

Expert Solution
Check Mark
To determine

The work of a force.

Answer to Problem 1PP

The work done by the force on the block is 160J .

Explanation of Solution

Given:

The force acting on the block is F=100N .

The displacement of the block is s=2m .

Draw the free body diagram of block as shown in Figure (g).

Engineering Mechanics: Dynamics (14th Edition), Chapter 14.3, Problem 1PP , additional homework tip  8

Write the formula for work done force (F) .

UF=Fs (I)

Here, F is the force and s is the displacement of the block.

Conclusion:

Refer Figure (g).

Resolve the force along xaxis .

F=100N(45)=80N

Substitute 80N for F and 2m for s in Equation (I).

UF=80N(2m)=160Nm×1J1Nm=160J

Thus, the work done by the force on the block is 160J .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A constant force of 512 N was done on an object. If it is known that 1024 Joules of energy was applied on it, determine the distance the object must travel along the line of action in meters.
Determine the work done by a locomotive in drawing a freight train for 1 mi at constant speed on a level track if the locomotive exerts a constant force of 6000 lb on the train.
A catapult is used to throw large projectiles by the ancient civilization. If a catapult swung from rest position and shot a 10-kg projectile at a velocity of 50 meters per second. Determine the force in Newtons exerted by the catapult on the projectile.

Chapter 14 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - Determine the required height h of the roller...Ch. 14.3 - How far will the truck skid if it is traveling 80...Ch. 14.3 - Show that this is so, by considering the 10-kg...Ch. 14.3 - A force of F = 250 N is applied to the end at B....Ch. 14.3 - If the block has a mass of 20 kg and is suspended...Ch. 14.3 - Determine how far the block must slide before its...Ch. 14.3 - If the 6-kg collar is orginally at rest, determine...Ch. 14.3 - Select the proper value of k so that the maximum...Ch. 14.3 - Determine the speed of the brick just before it...Ch. 14.3 - Determine the speed of block A after it moves 5 ft...Ch. 14.3 - If the kinetic coefficient of friction between the...Ch. 14.3 - Determine the angle at which the box leaves the...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - Determine the maximum distance A will fall before...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - The barrier stopping force is measured versus the...Ch. 14.3 - The coefficient of kinetic friction between both...Ch. 14.3 - If the coefficient of kinetic friction between the...Ch. 14.3 - The 8-Kg block is moving with an initial speed of...Ch. 14.3 - At a given instant the 10-lb block A is moving...Ch. 14.3 - The 5-lb cylinder is falling from A with a speed...Ch. 14.3 - The propelling action is obtained by drawing the...Ch. 14.3 - By design the car cannot fall off the track,...Ch. 14.3 - If the coefficient of kinetic friction along AB is...Ch. 14.3 - Prob. 29PCh. 14.3 - If the can is prevented from moving, determine the...Ch. 14.3 - Determine the placement R of the can from the end...Ch. 14.3 - If it starts from rest when the attached spring is...Ch. 14.3 - Neglect the size of the block.Ch. 14.3 - As shown, the spring is confined by the plate P...Ch. 14.3 - Determine his speed when he reaches point B on the...Ch. 14.3 - As shown, it is confined by the plate and wall...Ch. 14.3 - If the track is to be designed so that the...Ch. 14.3 - Neglect friction.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - An elastic cord having a stiffness k = 2 lb/ft is...Ch. 14.4 - In initially, the block is at rest.Ch. 14.4 - When s = 0, the 20-kg block is moving at v = 1...Ch. 14.4 - The load weighs 100 lb and the efficiency of the...Ch. 14.4 - If the block is traveling up the inclined plane...Ch. 14.4 - determine the power input to the motor, which...Ch. 14.4 - which is increasing at a rate of aP = 6 m/s2....Ch. 14.4 - Assuming the wheels do not slip on the ground,...Ch. 14.4 - Determine the power Input for a motor necessary to...Ch. 14.4 - If mechanical friction and wind resistance are...Ch. 14.4 - manufactures a turbojet engine that is placed in a...Ch. 14.4 - If the car is brought to a stop, determine how...Ch. 14.4 - If the steps are 125 mm high and 250 mm in length,...Ch. 14.4 - Determine the power generated. How long would a...Ch. 14.4 - Determine the maximum power that must be supplied...Ch. 14.4 - The cable is tied to the top of the oil rig, wraps...Ch. 14.4 - The motor has an efficiency of = 0.65.Ch. 14.4 - The 50-lb crate is given a speed of 10ft/s in t =...Ch. 14.4 - The engine has a running efficiency = 0.68.Ch. 14.4 - If the drag resistance on the car due to the wind...Ch. 14.4 - Hoisting is provided by the motor M and the 60-kg...Ch. 14.4 - If the rod is smooth, determine the power...Ch. 14.4 - Determine the power developed by the power...Ch. 14.4 - A force F = (40 + s2) lb, where sis in ft, acts on...Ch. 14.4 - If the steps are 125 mm high and 250 mm in length,...Ch. 14.4 - If the escalator in Prob.14-46 is not moving,...Ch. 14.4 - Neglect drag and rolling resistance, and the loss...Ch. 14.4 - Also, the velocity of the athletes arm acting in...Ch. 14.4 - Prob. 63PCh. 14.4 - If the motor draws in the cable at a constant rate...Ch. 14.5 - If a force F = (60t2) N, where t is in seconds, is...Ch. 14.5 - Determine the potential energy of the block that...Ch. 14.5 - Determine the potential energy in the spring that...Ch. 14.5 - The 2-kg pendulum bob is released from rest when...Ch. 14.5 - The 2-kg package leaves the conveyor belt at A...Ch. 14.5 - The 2-kg collar is given a downward velocity of 4...Ch. 14.5 - Determine the speed of the collar when it strikes...Ch. 14.5 - Determine the compression of each spring when the...Ch. 14.5 - If the guide rod is smooth, determine the speed of...Ch. 14.5 - If she is swinging to a maximum height defined by ...Ch. 14.5 - If it is then released, determine the maximum...Ch. 14.5 - Determine the speed of the collar when it reaches...Ch. 14.5 - Determine its speed when its center reaches point...Ch. 14.5 - If it is released from rest when = 0, determine...Ch. 14.5 - If the car is released from rest, determine its...Ch. 14.5 - Prob. 72PCh. 14.5 - If it is released from rest at the top of the hill...Ch. 14.5 - Determine the speed of each block when B descends...Ch. 14.5 - Determine the distance B must descend in order for...Ch. 14.5 - The spring has a stiffness k =50 N/m and an...Ch. 14.5 - Neglect friction.Ch. 14.5 - If it is attached to the 3-kg smooth collar and...Ch. 14.5 - Prob. 79PCh. 14.5 - If the arm is pulled back such that s = 100 mm and...Ch. 14.5 - If the arm is pulled back such that s = 100 mm and...Ch. 14.5 - For the calculation, locate the datum at r . Also,...Ch. 14.5 - Prob. 83PCh. 14.5 - The spring has an unstretched length of 1 m.Ch. 14.5 - A 60-kg satellite travels in free flight along an...Ch. 14.5 - If friction and air resistance can be neglected,...Ch. 14.5 - If the mass of the bumpers A and B can be...Ch. 14.5 - If the collar moves over the smooth rod, determine...Ch. 14.5 - When the 6-kg box reaches point A it has a speed...Ch. 14.5 - Determine the normal force the box exerts on the...Ch. 14.5 - Determine how high the box reaches up the surface...Ch. 14.5 - Determine the cars velocity and the normal force...Ch. 14.5 - The 10-kg sphere C is released from rest when =...Ch. 14.5 - If the chain is released from rest from the...Ch. 14.5 - Each spring has a stiffness k = 40 N/m and an...Ch. 14.5 - Prob. 96PCh. 14.5 - Initially each spring has a tension of 50 NCh. 14.5 - Determine the approximate normal force it exerts...Ch. 14.5 - If a 150-lb crate is released from rest at A,...Ch. 14.5 - During the motion, the collar is acted upon by a...Ch. 14.5 - Determine the speed at which it slides off at B....Ch. 14.5 - If the block starts from rest when the attached...Ch. 14.5 - Prob. 5RPCh. 14.5 - The motor has an efficiency of = 0.76.Ch. 14.5 - If the collar is released from rest at A and...Ch. 14.5 - respectively. They are connected together by a...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
Power Transmission; Author: Terry Brown Mechanical Engineering;https://www.youtube.com/watch?v=YVm4LNVp1vA;License: Standard Youtube License