A young boy is pulling his wooden toboggan up a 30 slope. If the toboggan is moving at a constant speed on the dry snow of the slope, calculate the minimum force the boy must exert in order to pull the toboggan, if the mass of the toboggan is 15 kg. The coefficient of kinetic friction is 0.18. (Hint: There will be two forces acting to pull the toboggan downhill!)

Question

A young boy is pulling his wooden toboggan up a 30 slope. If the toboggan is moving at a constant speed on the dry snow of the slope, calculate the minimum force the boy must exert in order to pull the toboggan, if the mass of the toboggan is 15 kg. The coefficient of kinetic friction is 0.18. (Hint: There will be two forces acting to pull the toboggan downhill!)

Answer 1

To calculate the minimum force the boy must exert in order to pull the toboggan up the slope, we need to consider the forces acting on the toboggan.

There are two forces acting on the toboggan: the force of gravity pulling it downhill and the force of friction opposing its motion. Since the toboggan is moving at a constant speed, we know that the net force acting on it is zero.

First, let's determine the force of gravity pulling the toboggan downhill. The force of gravity can be calculated using the formula:

Force of gravity = mass * acceleration due to gravity

Given that the mass of the toboggan is 15 kg and the acceleration due to gravity is 9.8 m/s², the force of gravity can be calculated as:

Force of gravity = 15 kg * 9.8 m/s² = 147 N

Next, let's determine the force of friction opposing the motion of the toboggan. The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

The normal force is the force exerted by the slope perpendicular to the surface. In this case, it is equal to the component of the force of gravity that is perpendicular to the slope.

Normal force = force of gravity * cosθ

Where θ is the angle of the slope. Given that the slope angle is 30°, we can calculate the normal force as:

Normal force = 147 N * cos(30°) = 147 N * 0.866 = 127.9 N

Now we can calculate the force of friction using the coefficient of friction. Given that the coefficient of kinetic friction is 0.18, the force of friction can be calculated as:

Force of friction = 0.18 * 127.9 N = 23.0 N

Since the net force on the toboggan is zero, and the force of friction is acting against the motion, the force the boy must exert to pull the toboggan uphill is equal to the force of friction:

Minimum force exerted by the boy = 23.0 N

Therefore, the minimum force the boy must exert to pull the toboggan uphill is 23.0 N.