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deng
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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?