A 52 kg skier is at the top of a slope, as in the
figure. At the initial point A, the skier is 12.4 m vertically above the final point B.
The acceleration of gravity is 9.81 m/s2 .Find the difference in potential energy if
the zero level is midway down the slope, at a
height of 6.20 m.
Answer in units of J.
The difference in potential energy between A and B does not depend upon where you define the zero level to be.
It is M g H, where H is the vertical distance between the two positions.
It is not clear if they are asking for the PE difference between A and B or between A and the midway point.
To find the difference in potential energy, we need to calculate the potential energy at point A and point B, and then subtract the potential energy at point B from point A.
The formula for gravitational potential energy is:
PE = m * g * h
where PE is the potential energy, m is the mass of the skier, g is the acceleration due to gravity, and h is the height.
Given information:
- Mass of the skier (m) = 52 kg
- Acceleration due to gravity (g) = 9.81 m/s^2
- Height at point A (hA) = 12.4 m
- Height at point B (hB) = 6.20 m (since the zero level is midway down the slope)
Calculate potential energy at point A:
PEA = m * g * hA
Substitute the values:
PEA = 52 kg * 9.81 m/s^2 * 12.4 m
Calculate potential energy at point B:
PEB = m * g * hB
Substitute the values:
PEB = 52 kg * 9.81 m/s^2 * 6.20 m
Now, calculate the difference in potential energy:
Difference in potential energy (PE_diff) = PEA - PEB
Substitute the values:
PE_diff = (52 kg * 9.81 m/s^2 * 12.4 m) - (52 kg * 9.81 m/s^2 * 6.20 m)
Calculate the difference in potential energy to get the answer in joules (J).