Problem Graphic

At the ACME factory, crates containing precious goods are carried through the plant on conveyor belts. When a conveyor belt stops, the boxes must not slide or the goods may be damaged.

What is known:

• The conveyor belts move at a constant speed of 10 ft/s.
• The crates first travel on a horizontal belt, then down a belt with a 15^o decline.
• The static, μ_s, and kinetic (dynamic), μ_k, coefficient of friction, μ_s, between the belt and the crates are = 0.5 and 0.3, respectively.

What is the shortest distance in which the horizontal belt can be brought to a stop without causing the crates to slide?

What is the shortest distance for the inclined belt?

• Using Newton's Second Law, relate the forces acting on the crate with its acceleration.
• Analyze the problem in terms of rectangular coordinates.
• Since no sliding actually occurs, use the static coefficient of friction.
• Derive an equation for the position by integrating the acceleration equation a = d²x/dt².