Question

A crate of mass 100.0 kg rests on a rough surface inclined at an angle of 37.0° with the horizontal. The coefficient of friction is 80% of that for the static case.

(a) What is the coefficient of static friction?
(b) What is the maximum force that can be applied upward along the plane on the rope and not move the block?
(c) With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed?
(d) If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction?
(e) Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?

Answer 1

Finding an exact coefficient of static friction requires additional information; however, we can discuss the maximum applied force, the acceleration, and the necessary forces for constant velocity both up the inclined plane and for preventing acceleration down the plane.

Step-by-step explanation:

Understanding Coefficient of Friction and Forces on an Inclined Plane

A crate of mass 100.0 kg is on a surface inclined at 37.0° with the horizontal. Given the coefficient of kinetic friction is 80% that of static friction, we will identify the static friction coefficient, the maximum applied force to prevent movement, the acceleration and required force for constant speed movement upwards, and the acceleration and required force to prevent acceleration downwards.

• (a) To determine the coefficient of static friction (μ_s), we need more information, as 80% alone does not provide an absolute value.
• (b) The maximum force upward along the plane is the force that overcomes both gravity's component down the slope and the maximum static friction.
• (c) Once moving, the acceleration can be determined by the net force and Newton's second law. A reduced force, equal to kinetic friction, is necessary for constant speed.
• (d) The acceleration down the plane is influenced by gravity and kinetic friction.
• (e) To prevent downward acceleration, the upward force must balance out gravity's component and kinetic friction.

For exact calculations, numerical values for coefficients of friction and gravitational acceleration would be required.