A crate rests on a rough ramp that is inclined at an angle of above the horizontal
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A 12kg crate rests on a rough ramp that is inclined at an angle of 18∘ above the horizontal. The coefficient of static friction between the crate and the ramp is 0.42. A worker plans to attach a light, inextensible cable to the crate and pull parallel to the surface of the ramp, acting up the incline.
Answer the following in sequence, showing complete reasoning and including appropriate units.
(a) Draw a free-body diagram for the crate, clearly labeling all forces that act on it while it remains at rest.
(b) Derive an algebraic expression for the smallest tension Tmin in the cable that will cause the crate to begin sliding up the ramp.
(c) Calculate Tmin using the numerical data provided.
(d) Suppose instead that the cable is used to pull the crate down the ramp (still parallel to the surface). Determine the smallest tension required to start the crate sliding downward, and discuss why this value differs from the result in part (c).