Block Sliding on Moving Cart: Determining Time and Distance with Friction Forces

[deng]

Homework Statement

A block is sitting on top of a cart (block A). The cart is being pulled at 200N to the right.
If a force F = 200N is applied to the 30 kg, cart, show that the 20kg block A will slide on the cart. Also determione the time for the block A to move on the cart 1.5m. The coefficients of static and kinetic frition between the block and the cart are us(static) = 0.3, uk(kinetic)= 0.25. Both cart at block start from rest.

Homework Equations

F=ma
force of friction f=usmg (for static friction)
force of friction f=ukmg (for kinetic friction)
xf = final position, x0= initial position,
xf=x0 + v0t + 1/2at^2

The Attempt at a Solution

I assumed that if the force is acting to the right on the cart, that it would be acting to the left on the the box. So when I do a free body diagram of the box I have F=200N going to the left, and f=usmg going to the right.
To prove that it will move I just show that 200>usmg, which it is when you plug in the numbers given.
To find how far it moves I just said:
F-f=ma
so
200-ukmg = max and since I'm only looking at the box I use the 20kg.
200-(0.25)(20)(9.81) = 20a
a= 7.547

then I plugged this acceleration into
xf = x0 + v0t + 1/2at^2
x0 = 0, v0 = 0 so it simplifies to
xf = 1/2at^2
1.5m = 1/2(7.547)t^2
and t = 0.6304 s.

Apparently the answer is 1.080s.

What am I doing wrong?

 

[RTW69]

For Part a: Assume block A does not slide on the cart and find u_s. If it is less than 0.3 you know the block slides. You will need to do free body diagrams for both block A and the cart. Both are accelerating to the right in part a.

After you have convinced yourself that the block moves redo with u_k=0.25.

 

[RTW69]

I don't see a 200 N force on block A. I see a Ff, mg and N_A force and an acceleration.