A 60.0 kg skier rides a 2740 m long lift to the top of a mountain. The lift makes an angle of 14.7¡ã with the horizontal. What is the change in the skier's gravitational potential energy?
P.E change = M g H
H is the change in elevation, 2740 sin 14.7 meters
g = 9.8 m/s^2
M = 60.0 kg
75.0-kg skier rides a 2730-m-long lift to the top of a mountain. The lift makes an angle of 12.0° with the horizontal. What is the change in the skier’s gravitational potential energy?
To calculate the change in the skier's gravitational potential energy, we need to consider the change in height and the skier's mass.
First, let's find the change in height. We know the length of the lift, which is 2740 m, and the angle it makes with the horizontal, which is 14.7°. We can use trigonometry to find the vertical component of the lift's length:
Vertical component = Length of lift * sin(angle)
= 2740 m * sin(14.7°)
Next, we need to find the gravitational potential energy. The gravitational potential energy formula is given by:
Gravitational potential energy = mass * g * height
where mass is the skier's mass (60.0 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and height is the change in height.
Change in gravitational potential energy = mass * g * change in height
Now, let's plug in the values:
Change in gravitational potential energy = 60.0 kg * 9.8 m/s² * (vertical component)
Calculating this expression will give us the change in the skier's gravitational potential energy.