Question

You want to use a rope to pull a 12-kg box of books up a plane inclined 30∘ above the horizontal. The coefficient of kinetic friction is 0.27. The rope pulls parallel to the incline. What force do you need to exert on the rope if you want to pull the box at constant speed.What force do you need to exert on the rope if you want to pull the box at constant speed?

A. 117.6 N
B. 105.3 N
C. 98.1 N
D. 82.4 N

Answer 1

To pull the box at constant speed, the force needed is equal to the force of friction. Using the given information, the force needed to pull the box in this scenario is approximately 105.3 N.

Step-by-step explanation:

To find the force needed to pull the box at constant speed, we need to analyze the forces acting on the box. First, we find the weight of the box, which is given by the equation: weight = mass × gravity. In this case, the mass of the box is given as 12 kg, so the weight is 12 kg × 9.8 m/s² = 117.6 N. Next, we find the force of friction, which is calculated using the equation: force of friction = coefficient of friction × normal force. The normal force is equal to the weight of the box multiplied by the cosine of the angle of inclination. Substituting the given values, we get: normal force = 117.6 N × cos(30∘) ≈ 101.96 N. Finally, we can find the force needed to pull the box at constant speed by summing up all the forces acting on the box along the incline and setting it equal to zero. The force needed to pull the box at constant speed is equal to the force of friction. Therefore, the answer is option B. 105.3 N.