A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration 0.84 m/s2 directed down the ramp. The ramp makes an angle of 42° with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?

0.785

Explanation:

Given:

Acceleration of the canned goods down the ramp (a) = 0.84 m/s²

Angle of inclination of ramp (x) = 42°

Acceleration due to gravity (g) = 9.8 m/s²

Let the coefficient of kinetic friction between the box and the ramp be 'μ'.

Draw a free body diagram of the box and label the forces along the ramp and perpendicular to the ramp.

From the diagram,

Normal force is given as:

So, frictional force is given as:

Also, from the diagram, the net force along the ramp is given as:

Now, from Newton's second law, net force is equal to the product of mass and acceleration. So,

Now, plug in the given values and solve for 'μ'. This gives,

Therefore, the coefficient of kinetic friction between the box and the ramp is 0.785.

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explanation:

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