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Chapter 5: Problem 26

You push your couch a distance of \(4.00 \mathrm{~m}\) across the living room floor with a horizontal force of \(200.0 \mathrm{~N}\). The force of friction is \(150.0 \mathrm{~N}\). What is the work done by you, by the friction force, by gravity, and by the net force?

Short Answer

Expert verified
Answer: The work done by the applied force (you) is 800.0 J, the work done by the friction force is -600.0 J, the work done by the force of gravity is 0 J, and the work done by the net force is 200.0 J.

Step by step solution

01

Calculate the work done by the applied force (you)

Using the work formula and the given data, we have: Work = (200.0 N) 脳 (4.00 m) 脳 cos(0) Since cos(0) = 1, Work = 200.0 N 脳 4.00 m = 800.0 J The work done by the applied force (you) is 800.0 J.
02

Calculate the work done by the friction force

Again, using the work formula and the given data, we have: Work = (150.0 N) 脳 (4.00 m) 脳 cos(180) Since cos(180) = -1, Work = 150.0 N 脳 4.00 m 脳 -1 = -600.0 J The work done by the friction force is -600.0 J.
03

Calculate the work done by the force of gravity

Since the force of gravity is acting perpendicular to the direction of displacement, the angle between them is 90 degrees. Therefore, we have: Work = Force 脳 Distance 脳 cos(90) Since cos(90) = 0, Work = Force 脳 Distance 脳 0 = 0 The work done by the force of gravity is 0 J.
04

Calculate the net force acting on the couch

The net force acting on the couch can be determined by subtracting the force of friction from the applied force: Net force = Force_applied - Force_friction = 200.0 N - 150.0 N = 50.0 N The net force acting on the couch is 50.0 N.
05

Calculate the work done by the net force

Now that we have the net force, we can calculate the work done using the work formula: Work = (50.0 N) 脳 (4.00 m) 脳 cos(0) Since cos(0) = 1, Work = 50.0 N 脳 4.00 m = 200.0 J The work done by the net force is 200.0 J. In summary, the work done by the applied force (you) is 800.0 J, the work done by the friction force is -600.0 J, the work done by the force of gravity is 0 J, and the work done by the net force is 200.0 J.

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Most popular questions from this chapter

An \(800-\mathrm{N}\) box is pushed up an inclined plane that is \(4.0 \mathrm{~m}\) long. It requires \(3200 \mathrm{~J}\) of work to get the box to the top of the plane, which is \(2.0 \mathrm{~m}\) above the base. What is the magnitude of the average friction force on the box? (Assume the box starts at rest and ends at rest.) a) \(0 \mathrm{~N}\) c) greater than \(400 \mathrm{~N}\) b) not zero but d) \(400 \mathrm{~N}\) less than \(400 \mathrm{~N}\) e) \(800 \mathrm{~N}\)

An engine pumps water continuously through a hose. If the speed with which the water passes through the hose nozzle is \(v\) and if \(k\) is the mass per unit length of the water jet as it leaves the nozzle, what is the kinetic energy being imparted to the water? a) \(\frac{1}{2} k v^{3}\) c) \(\frac{1}{2} k v\) e) \(\frac{1}{2} v^{3} / k\) b) \(\frac{1}{2} k v^{2}\) d) \(\frac{1}{2} v^{2} / k\)

A \(65-\mathrm{kg}\) hiker climbs to the second base camp on Nanga Parbat in Pakistan, at an altitude of \(3900 \mathrm{~m}\), starting from the first base camp at \(2200 \mathrm{~m}\). The climb is made in \(5.0 \mathrm{~h}\). Calculate (a) the work done against gravity, (b) the average power output, and (c) the rate of energy input required, assuming the energy conversion efficiency of the human body is \(15 \%\)

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If the net work done on a particle is zero, what can be said about the particle's speed?
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