Physic C_again!!!!!!!!!!!!!!!

Question

1./ What is the greatest acceleration that can be generated by a runner if the coefficient of static friction between shoes and track is 0.95 (Only one foot is on the track during the acceleration???

2./ A 4.0 kg block is put on top of a 5.0 kg block. To cause the top block to slip on the bottom one, while the bottom one is held fixed, a horizontal force of at least 12N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table. Find (a) the magnitude of the maximum horizontal force F the can be applied ti the lower block so that the blocks will move together and (b) the resulting acceleration of the blocks.

Answer 1

1. The only force acting on the runner is the frictional force, f.

f = coefficient of friction * mg  = 0.95 mg

Acceleration = f / m = 0.95 g = 9.31 m/s^2

2. Applied force on 4 kg block = 12 N

This force is equal to the maximum frictional force f since it is the minimum force required to move the block.

Normal reaction, N = mg = 4*g

So mu = f/N = 0.3

Now both the blocks will move together if both have the same acceleration.

Assume that the force is applied from the left.

Consider 4 kg block:

The forces on it are:

mg acting dwnwards

Normal reaction from 5 kg block N' acting upwards

Since the 5 kg block is trying to move towards right due t the applied force, the frictional force, f is trying to prevent their relative motion.

So f is acting towards right.

Maximum value of f = mu * mg

a = f / m = mu * m = 1.2

You don't need to consider the vertical forces since the motion of the blocks is only in the horizontal direction.

Consider 5 kg block :

I am ignoring vertical forces as they cancel out each other.

Applied force F acts towards right.

a = F / m = F / 5            

So

1.2 = F / 5

F = 6 N

a = F / 5 = 1.2 m/s^2

Hope this helps.

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