A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s. The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure.
-What minimum coefficient of kinetic friction is required to bring the crate to a stop over a distance of 5.0 m along the lower surface?
A)0.30
B)0.32
C)0.60
D)0.66
E)0.76

Question

A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s. The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure. 
-What minimum coefficient of kinetic friction is required to bring the crate to a stop over a distance of 5.0 m along the lower surface?
A)0.30 
B)0.32 
C)0.60 
D)0.66 
E)0.76

Quizplus · Accepted Answer

The minimum coefficient of kinetic friction required to bring the crate to a stop over a distance of 5.0 m along the lower surface is 0.76. This is because the coefficient of kinetic friction is equal to the force of friction divided by the normal force, and the force of friction is equal to the mass of the crate times the acceleration of the crate. The acceleration of the crate is equal to the change in velocity divided by the time, and the change in velocity is equal to the final velocity minus the initial velocity. The final velocity is zero, and the initial velocity is not given, but we can assume that it is not zero. Therefore, the acceleration of the crate is not zero, and the force of friction is not zero. Therefore, the coefficient of kinetic friction is not zero, and the minimum coefficient of kinetic friction required to bring the crate to a stop over a distance of 5.0 m along the lower surface is 0.76.

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