Question

A block of weight 100 N is initially at rest on a horizontal surface. The coefficient of static friction between the block and the surface is 0.60. A horizontal force of 40 N directed to the right is then applied to the block. Will the block accelerate? If so, in which direction will it accelerate and what will be the magnitude of its acceleration? Justify your answer.

Answer 1

The block with a weight of 100 N will not accelerate when a horizontal force of 40 N is applied to it, as the applied force is less than the maximum static frictional force, which is calculated to be 60 N.

Step-by-step explanation:

When considering whether the block with a weight of 100 N will accelerate when a horizontal force of 40 N is applied, we must first calculate the maximum static frictional force that can act on the block. This force can be found by using the equation fs(max) = μsN, where 'μs' is the coefficient of static friction and 'N' is the normal force. For a block on a horizontal surface, the normal force is equal to the weight of the block, which is 100 N in this case. With a coefficient of static friction of 0.60, the maximum static frictional force is fs(max) = (0.60)(100 N) = 60 N.

Since the applied force of 40 N is less than the maximum static frictional force of 60 N, the block will not overcome static friction, and therefore, it will not accelerate. The block remains at rest, and there is no direction of acceleration or magnitude to be calculated because the static friction is sufficiently large to resist the motion.