A 750 kg skier rides a 2830 m long lift to the top of a mountain. The lift makes an angle of 14.6˚ with the horizontal. What is the change in the skier’s gravitational potential energy?
5.24 x 10^5 J
h = 2830sin14.6 = 713.4
mgh = 75*9.8*713.4 = 5.24e5 joules
To calculate the change in the skier's gravitational potential energy, we need to find the difference in height between the top and bottom of the lift.
The vertical height can be calculated using the length of the lift and the angle it makes with the horizontal.
Using trigonometry, we can find the vertical height:
sin(angle) = opposite / hypotenuse
Opposite side = hypotenuse * sin(angle)
Plugging in the values, we have:
Opposite side = 2830 m * sin(14.6˚)
Opposite side = 2830 m * 0.252687
Opposite side ≈ 714.26 m
Therefore, the change in the skier's gravitational potential energy is equal to the change in height, which is approximately 714.26 meters.
To find the change in the skier's gravitational potential energy, we need to calculate the difference in potential energy between the top and the bottom of the lift.
First, let's calculate the height difference, which is the vertical component of the distance traveled by the lift. We can do this by multiplying the total distance by the sine of the angle between the lift and the horizontal:
Height difference = 2830 m * sin(14.6°)
Next, we can use the formula for gravitational potential energy:
ΔPE = m * g * h
where ΔPE is the change in potential energy, m is the mass of the skier, g is the acceleration due to gravity, and h is the height difference.
The acceleration due to gravity, g, is approximately 9.8 m/s².
Substituting the values into the formula:
ΔPE = 750 kg * 9.8 m/s² * height difference
Calculating the final result will give us the change in the skier's gravitational potential energy.