A box slides down a 30.0° ramp with an acceleration of 1.20 m/s^2. Determine the coefficient of kinetic friction between the box and the ramp.

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Question:

A box slides down a 30.0° ramp with an acceleration of 1.20 m/s^2. Determine the coefficient of kinetic friction between the box and the ramp.

Answer:

The coefficient of kinetic friction between the box and the ramp is 0.71.

Given data:

The angle of inclination is, ?f=%5Ctheta%20%3D%2030%5E%5Ccirc.

The acceleration of box is, ?f=a%20%3D%201.

The frictional force acting on the box is,

?f=f%3D%20%5Cmu%20%5Ctimes%20N

Here, ?f=%5Cmu is the coefficient of kinetic friction and N is the normal force.

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The normal force in an inclined plane is,

?f=N%3Dmg%20cos%5Ctheta

Since the frictional force causes the acceleration (a) of box,

?f=F%3Df mgsin%5Ctheta%5C%5Cma%3D%5Cmu%20mgcos%5Ctheta mgsin%5Ctheta%5C%5Ca%3D%5Cmu%20gcos%5Ctheta gsin%5Ctheta

Solving as,

?f=a%3D%5Cmu%20gcos%5Ctheta gsin%5Ctheta%5C%5C%5Cmu%3D%5Cdfrac%7Ba%2Bgsin%5Ctheta%7D%7Bgcos%5Ctheta%7D%20%5C%5C%5Cmu%3D%5Cdfrac%7B1.20%2B9.8sin30%7D%7B9.8cos30%7D%5C%5C%5Cmu%3D%200

Thus, the coefficient of kinetic friction between the box and the ramp is 0.71.

Learn more about frictional force here:

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