5. A 3.00 kg mass is initially at rest at the bottom of an incline of 35.0°. An applied force beginsacting on the mass, pushing it up the incline with a constant force of 25.0 N, directed parallel tothe incline.a) If the acceleration produced is 2.50 m/s? up the incline, what must the coefficient of kineticfriction be?b) If the applied force acts for 2.00 s, how far up the incline will the mass travel upon coming torest? Measure this from where the applied force starts acting to where the mass comes to a stop.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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5. A 3.00 kg mass is initially at rest at the bottom of an incline of 35.0°. An applied force begins
acting on the mass, pushing it up the incline with a constant force of 25.0 N, directed parallel to
the incline.
a) If the acceleration produced is 2.50 m/s? up the incline, what must the coefficient of kinetic
friction be?
b) If the applied force acts for 2.00 s, how far up the incline will the mass travel upon coming to
rest? Measure this from where the applied force starts acting to where the mass comes to a stop.

Expert Solution

Step 1

The free body diagram of the mass is given below.

(a)

Express the relation for the frictional force between the incline and the mass.

$\begin{array}{rcl} F_{k} & = & μ_{k} R \\ = & μ_{k} m g \cos θ \end{array}$

Here, F_k is the frictional force, R is the normal reaction, μ_k is the coefficient of kinetic friction, m is the mass, g is the acceleration due to gravity and θ is the angle of inclination of the incline.

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