Question

To understand kinetic and static friction. A block of mass m lies on a horizontal table. The coefficient of static friction between the block and the table is μs. The coefficient of kinetic friction is μk, with μk<μs.

a-

Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what force F must you be pushing the block just before the block begins to move?

Express the magnitude of F in terms of some or all the variables μs, μk, and m, as well as the acceleration due to gravity g.

b-Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force?

Express your answer in terms of some or all of the variables μs, μk, and m, as well as the acceleration due to gravity g.

c-

Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration a of the block after it begins to move.

Express your answer in terms of some or all of the variables μs, μk, and m, as well as the acceleration due to gravity g.

Answer 1

Part A: The minimum force required to move the block is equal to the force of limiting friction (static friction force) Thus, the force required to applv is: 011 min = μ.N Part B: To minimize the minimum force required to move the block, the force due to static friction must be reduced to half Thus. the magnitude of friction force 1s: Fmi.. μ.rng _ Part C: Minimum force required to move the block is: rain_ μ.mg Once the block under goes into the motion, the minimum force required to keep it in motion is 0 11 The net force with which the block moves is 011 011 ma -(u,-)mg