A 60.0 kg skier rides a 2710 m long lift to the top of a mountain. The lift makes an angle of 14.5° with the horizontal. What is the change in the skier's gravitational potential energy?
To find the change in the skier's gravitational potential energy, we need to first calculate the initial and final potential energies.
The formula for calculating potential energy is:
Potential Energy = mass * gravitational acceleration * height
Since the skier rides a lift to the top of the mountain, the only change in height that affects potential energy is the vertical component of the lift's displacement. To find this vertical displacement, we need to find the height difference caused by the angle of the lift.
We can calculate the vertical displacement using the formula:
Vertical Displacement = lift length * sin(angle)
Now we have all the necessary information to calculate the change in the skier's gravitational potential energy.
First, let's calculate the vertical displacement:
Vertical Displacement = 2710 m * sin(14.5°)
Now, let's calculate the initial and final potential energies:
Initial Potential Energy = mass * gravitational acceleration * height_initial
Final Potential Energy = mass * gravitational acceleration * height_final
Since the skier is at the top of the mountain, the initial potential energy will be zero. Therefore, the change in potential energy will be equal to the final potential energy:
Change in Potential Energy = Final Potential Energy = mass * gravitational acceleration * height_final
Substituting the given values:
Change in Potential Energy = (60.0 kg * 9.8 m/s^2 * Vertical Displacement)
Calculate the Vertical Displacement from earlier and calculate the final numerical value of Change in Potential Energy.