# Solving Work and Force of Wagon and Child

A child pulls a wagon with a force of 100N on a rope that makes a sixty degree angle with a horizontal floor. He pulls the wagon a distance of 25 meters along the floor. A: how much force is done in the direction that the wagon moves? B: How much work does the child do?

W = FD
W = FDCosθ

A: W = FD

= (100)(25)
= 2500 Joules done in the direction that the wagon moves

B: W = FDCosθ

= (100)(25)Cos60
= 1250 Joules

Did I setup and solve these problems correctly?

## The Attempt at a Solution

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CAF123
Gold Member
B is right, but A is not. A is looking for a force but you found work.

Is this the force that you are supposed to use for B or are you supposed to use the force that you are supposed to solve for?

CAF123
Gold Member
Is this the force that you are supposed to use for B
Yes

or are you supposed to use the force that you are supposed to solve for?
??

Is there a separate equation I need to solve for the force in part A ? I assume the force they are asking for isn't given in the information. Referring to my question above should the 100 N be used for part B or should for force found in part A be used?

CAF123
Gold Member
Is there a separate equation I need to solve for the force in part A ? I assume the force they are asking for isn't given in the information. Referring to my question above should the 100 N be used for part B or should for force found in part A be used?
Only force in direction of displacement contributes work. The force applied is at an angle to the horizontal so for part A, you need to find the component of this force in the direction of motion.
You computed B correctly, which means you effectively already have the answer.

I thought I understood your answer but I do not think I did. I used W=FD 1250=F(25)
F=50N

That does not seem correct

Doc Al
Mentor
Think of your formula for work as W = (Fcosθ)*D

What does Fcosθ represent?

The force in the direction it is being pulled? Which is equal to 50 Joules

Doc Al
Mentor
The force in the direction it is being pulled?
Right. Which is what part A asks for.

Which is equal to 50 Joules
Newtons, not Joules. (Newton the unit of force; Joule the unit of energy.)

I guess I solved wrong but got the correct answer? Because I did W = F * Cos60

W = 100 * Cos60
W = 50 joules