What is the acceleration of the cart? :)

[Dusty912]

Homework Statement

A man is pulling himself up the 15 degree incline by the method shown. If the combined mass of the man and the cart is 100kg, determine the acceleration of the cart if the man excerpts 250 N on the rope. There is also a .2 coefficient for the kinetic friction between the wheels and the ground.

Homework Equations

F=m*a
F_k=μ*N

The Attempt at a Solution

So I pretty much know how to solve this without friction being involved. Where T is the friction in the rope, m is the mass of the man and cart theta is the angle, and a is acceleration.

F=m*a
4T-m*g*sinθ=m*a

now when you throw friction into the mix should it look like this?
F=m*a
4T-m*g*sinθ-μ*N=m*a
4T-m*g*sinθ-μ*m*g*cosθ=m*a

with the numerical values
4*(250)-100*9.81*sin(15)-.2*100*9.81*cos(15)=100*a
a=5.566m/2^2Thanks ahead of time, you all rock

 

[TomHart]

by the method shown

Is there a figure you can attach?

 

[haruspex]

There is also a .2 coefficient for the kinetic friction between the wheels and the ground.

Sack the question setter. Presumably the wheels are rolling, so kinetic friction between them and the ground is irrelevant, and static friction would not cost any energy. It should say "rolling resistance", not friction. (0.2 is rather high.)

T is the friction in the rope

You mean tension, I assume.

4T

I infer that the pulley system involves four lengths of rope between the cart and the top of the slope. If so, your method and answer look fine.

 

[Dusty912]

 

[Dusty912]

yea, tension in the rope not friction

 

[Dusty912]

and are you saying the question is worded incorrectly? because that was a word for word question by professor wrote

 

[haruspex]

and are you saying the question is worded incorrectly? because that was a word for word question by professor wrote

Yes. See 4.1 in https://www.physicsforums.com/insights/frequently-made-errors-mechanics-friction/.

 

[Dusty912]

okay well thanks for pointing that out. we have a forum for our class, so I'll let others know.