A block of massĀ mĀ lies on a horizontal table. The coefficient of static friction between the block and the table isĀ Ī¼s. The coefficient of kinetic friction isĀ Ī¼k, withĀ Ī¼k<Ī¼s.
Part A
If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction?
Part B
Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what forceĀ FĀ must you be pushing the block just before the block begins to move?
Express the magnitude ofĀ F in terms of some or all the variables Ī¼s,Ī¼k, andĀ m, as well as the acceleration due to gravityĀ g.
Part C
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 Ī¼s, Ī¼k, andĀ m, as well as the acceleration due to gravityĀ g.
Part D
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 accelerationĀ aĀ of the block after it begins to move.
Express your answer in terms of some or all of the variables Ī¼s, Ī¼k, andĀ m, as well as the acceleration due to gravityĀ g.