A skier of mass 75 kg accelerates from rest down the slope as shown in the diagram (It's a triangle with a height of 300 m, length of 400 m, and the hypotenuse is 500 m; The skier is on the hypotenuse.
At the bottom of the slope, he is travelling at 40 m/s.
What is the average force opposing his motion down the slope?
Compute the kinetic energy gain and the potential energy loss. Take the difference. That is work done against opposing forces. That equals the average force times the slope length.
Solve for the average force.
To find the average force opposing the skier's motion down the slope, we need to use the concept of work and energy. The work done by the force opposing motion can be calculated by subtracting the initial kinetic energy from the final kinetic energy.
To calculate the initial kinetic energy (KE_initial) of the skier, we can use the formula:
KE_initial = (1/2) * mass * velocity_initial^2
Since the skier starts from rest, the initial velocity (velocity_initial) is 0. Therefore, the initial kinetic energy is 0.
To calculate the final kinetic energy (KE_final) of the skier, we can use the formula:
KE_final = (1/2) * mass * velocity_final^2
Given that the skier is traveling at a velocity (velocity_final) of 40 m/s, and the mass (mass) of the skier is 75 kg, we can calculate the final kinetic energy:
KE_final = (1/2) * 75 kg * (40 m/s)^2
Next, we can calculate the work done by the force opposing motion (work_opposing) using the equation:
work_opposing = KE_final - KE_initial
Since the initial kinetic energy is 0, the equation simplifies to:
work_opposing = KE_final
Now, let's calculate the final kinetic energy:
KE_final = (1/2) * 75 kg * (40 m/s)^2
KE_final = 0.5 * 75 kg * 1600 m^2/s^2
KE_final = 60000 J
Therefore, the work done by the force opposing motion is 60000 J.
To find the average force opposing the skier's motion, we can use the equation:
average force = work_opposing / distance
The distance traveled by the skier down the slope is given as 500 m (the hypotenuse of the triangle).
average force = 60000 J / 500 m
average force = 120 N
So, the average force opposing the skier's motion down the slope is 120 Newtons.