Question

1.A 4.5kg object is at rest on a table with state friction of 0.56 and kinetic friction of 0.46. A force is applied such that the object just beings to move. If that same force is maintained, at what rate will the object accelerate?
The answer is 0.98m/^2
2.A 2.0kg block is at rest on a table. At what rate will it accelerate when a force of 6.5N is exerted on the block?
The answer is 0m/^2
Can you please explain how to get those two answers? THANK YOU!

Answer 1

1. What you call "state" friction is the STATIC friction coefficient. After it starts moving, what you need to use is the kinetic friction coefficient, 0.46. Multiply that by the weight to get the kinetic friction force.
Fk = 0.46 M g = 20.29 N
The force that barely started it moving, and remained applied, is the static friction,
Fs = 0.56*M*g = 24.70 N
The net force applied is
Fnet = Fs - Fk = 4.41 N

The acceleration is a = Fnet/M
= 4.41/4.5 = 0.98 m/s^2

2. They expect you to assume that the static friction coefficient is the same as in the first problem. (This will be true is materials and surface roughnesses remain the same, even though the block has a smaller mass than in the previous problem.

The force required to make the block move is
0.56*2.0*9.8 = 10.98 N
Since a lesser force is applied, the block will not accelerate