# Work and Force Problem

• deserthobo
In summary, the given problem involves a cart with a mass of 16 kg being pushed by a woman at an angle of 29 degrees below the horizontal. The frictional force acting on the cart is 48 N. The woman's force is used to overcome the frictional force, resulting in a constant velocity. The problem involves finding the correct direction and magnitude of the woman's force, which can be achieved by drawing a force-body diagram and considering the net force of the system. The textbook answer of 54.9 N is obtained by taking the ratio of the frictional force to the woman's force, which is equal to the cosine of the given angle. The direction of the frictional force must be opposite to the direction of

## Homework Statement

http://img406.imageshack.us/img406/117/physicsprob3pp6.jpg [Broken]

known date
1. angle= 29 degrees
2. frictional force = 48 N
3. mass of cart = 16 kg
4. displacement = 22 meters
5. velocity = constant

## Homework Equations

F=ma
F(s)=mas
W=F cos theta (s)

## The Attempt at a Solution

this problem gave me a headache when i attempted to solve it. first i resolved that since velocity is constant, then a=0 but that would mean that the force = 0 and that would say that the person is not exerting any force on the cart. that's all i have down.

v=constant
a=0
F(s)=mas
0=0
whats the force she's exerting then? i know how to figure out work, that's easy. just use the work formula.

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so you know a). for b),c) and d) just draw a FBD for each.
hint: d) should be just mg.

i don't know a! my guess is a = 48 N but my textbook says 54.9. how the heck did it get that answer?

deserthobo said:
i don't know a! my guess is a = 48 N but my textbook says 54.9. how the heck did it get that answer?

48 N is the magnitude of the frictional force. Don't guess! Draw a force-body diagram and figure out how much force the person is exerting on the cart.

The ratio of 48/54.9 is cos( 29 degrees). Does that give you a clue ?

Mentz114 said:
The ratio of 48/54.9 is cos( 29 degrees). Does that give you a clue ?

wait i don't get it, doesn't the force of friction act opposite of the direction of the displacement and force that the person exerts? if that's the case then why am i using this ratio?

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hey guys i drew a free body diagram, can you tell me what's wrong

http://img88.imageshack.us/img88/2869/freebodyhu4.jpg [Broken]

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The direction of the frictional force is wrong.
You are missing two other forces.
If a is zero, then the NET force is zero, that is to say that when you add up all the forces (vectorially) the sum(net) is zero.

i really have no clue as to the direction of the frictional force

are the two other forces I am missing the normal force and w=mg? i don't i need those in this problem.

Yes, the other two forces I am referring to are the normal and gravity.
The path of the cart is on a horizontal surface. The frictional force opposes the motion.

it says that the woman is pushing the cart in a direction 29 degrees below the horizontal

I see, I have assumed that the motion of the cart is in the horizontal direction only. The problem does not seem to state that though, hmmm. Is there a picture that goes with the problem?

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Yea I was thinking the woman was foolishly pushing down when the cart was moving horizontally as well, but if she is on a hill, answer to a of 54.9 doesn't seem to fit, ie if she is pushing harder than the frictional force, the cart should accelerate, even gravity is helping her?

no picture to go with the problem.

well robb is offline, so I'll butt in and suggest that the situation per my last post is the cart is on a horizontal surface.

We know first that in order for there to be no acceleration, her force must exactly oppose the frictional force. If she were pushing horizontally, then 48N is the right answer. But she is pushing at an angle and only some of her force is used to overcome friction, and no we needn't worry yet about mg/normal forces, ie since we are given the total frictional force we needn't worry about its components. So redo the FBD only assume its moving horizontally. The rest should be fairly straightforward as there is no acceleration. Just need to consider force times displacement I think.

oooooh thanks a ton denverdoc, i guess i needed to read the problem more carefully. it was just confusing as rather the cart she was pushing was 29 degrees below the horizontal or the force she exerts on the cart is 29 degrees below...

Hey, lots of these guys who word these problems need to be put in a small room and forced to solve each others problems. :tongue:

Physics is tuff enuf w/o ambiguous wording of questions.

denverdoc said:
Hey, lots of these guys who word these problems need to be put in a small room and forced to solve each others problems. :tongue:

Physics is tuff enuf w/o ambiguous wording of questions.
Lol!