1. Here is the setup. A cart of mass M on frictionless wheels will be pushed wit

Q: 1. Here is the setup. A cart of mass M on frictionless wheels will be pushed wit

for m f = m*a us*m*g = m*a a = us*g ----------------- for M F - fs = Ma F - us*m*g = M*us*g F = us*g*(M+m) ----------------- a = F/(M+m) -------------- a1 = uk*g for M F - f = M*a2 a2 = 2a1 M = 2m F - uk*m*g = M*2*uk*g F = uk*g*(m+2M) F = uk*g*5*m

ID: 1586211 • Letter: 1

Question

1. Here is the setup. A cart of mass M on frictionless wheels will be pushed with a constant force F. A block of mass m is placed on top of the cart. There is friction between the cart and the block.

If the block does not slide against the cart,

a. What is the maximum acceleration of the block?

b. What is the maximum force the can be applied to the cart? If the block does slide against the cart,

c. What is the acceleration of the block?

d. What force is required to accelerate the cart at twice the acceleration of the block if the cart mass is twice that of the block?

m us and uk

Explanation / Answer

for m

f = m*a

us*m*g = m*a

a = us*g

-----------------

for M

F - fs = Ma

F - us*m*g = M*us*g

F = us*g*(M+m)

-----------------

a = F/(M+m)

--------------

a1 = uk*g

for M

F - f = M*a2

a2 = 2a1

M = 2m

F - uk*m*g = M*2*uk*g

F = uk*g*(m+2M)

F = uk*g*5*m

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1. Here is the setup. A cart of mass M on frictionless wheels will be pushed wit

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