Question

A box of mass m=19.0 kg is pulled up a ramp that is inclined at an angle θ=15.0∘ angle with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is μk=0.295 , and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of a=3.09 m/s2, calculate the tension FT in the rope. Use g=9.81 m/s2 for the acceleration due to gravity.

Answer 1

There are four forces acting on the box: mg is the gravitational force of Earth, T is the tension, N is the normal force applied by the ramp on the box, and F_{​​​​​​k} is the force of kinetic friction on the box. The friction force resist motion of the box along the ramp in the upward direction. The free body diagram of the box is shown below:

The box is not allowed to move in the direction perpendicular to the ramp, therefore, the net force in this direction must be zero

The force of kinetic friction on the box is

The net force along the incline accelerates the box.

Solving for tension

Substituting values