A 80.4-kg skier rides a 2630-m-long lift to the top of a mountain. The lift makes an angle of 19.4 ° with the horizontal. What is the change in the skier's gravitational potential energy?
m * g * h
80.4 * g * 2630 * sin(19.4º)
To determine the change in the skier's gravitational potential energy, we need to calculate the difference in potential energy between the top and bottom of the lift.
The formula to calculate the gravitational potential energy is given by:
PE = mgh
Where:
PE is the gravitational potential energy
m is the mass of the skier
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the vertical height or displacement
First, let's calculate the vertical height or displacement of the lift using trigonometry:
h = Length of Lift * sin(angle)
Plugging in the given values:
Length of Lift = 2630 m
Angle = 19.4 °
h = 2630 * sin(19.4 °)
Calculating this will give us the vertical height or displacement h.
Next, we can calculate the change in gravitational potential energy:
ΔPE = PE_top - PE_bottom
PE_top = m * g * h_top
PE_bottom = m * g * h_bottom
Since the skier starts at the bottom and goes to the top, the change in potential energy is:
ΔPE = PE_top - PE_bottom = (m * g * h_top) - (m * g * h_bottom)
Plugging in the given values:
m = 80.4 kg
g = 9.8 m/s^2
h_top = h (calculated using trigonometry)
h_bottom = 0 (since the skier starts at the bottom)
Calculating this will give us the change in the skier's gravitational potential energy.