A 52 kg skier is at the top of a slope, as in the
figure. At the initial point A, the skier is 17.7
m vertically above the final point B.
The acceleration of gravity is 9.81 m/s2 .
Find the difference in gravitational po-
tential energy associated with the skier at the
points A and B if the zero level for gravita-
tional potential energy is at point B.
Answer in units of J.
To find the difference in gravitational potential energy between points A and B, we need to calculate the potential energy at each point and then subtract the two values.
The gravitational potential energy can be calculated using the formula:
PE = mgh
where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the vertical height or the difference in height between the two points.
In this case, the mass of the skier is 52 kg, the acceleration due to gravity is 9.81 m/s^2, and the vertical height h is given as 17.7 m.
First, let's calculate the potential energy at point A:
PE_A = m * g * h_A
= 52 kg * 9.81 m/s^2 * 17.7 m
Next, we calculate the potential energy at point B:
PE_B = m * g * h_B
= 52 kg * 9.81 m/s^2 * 0 m (since the zero level for gravitational potential energy is at point B)
Finally, we find the difference in potential energy:
ΔPE = PE_A - PE_B
Calculating the values:
PE_A = 52 kg * 9.81 m/s^2 * 17.7 m
≈ 8,355.684 J
PE_B = 0 J (since h_B is 0)
ΔPE = 8,355.684 J - 0 J
≈ 8,355.684 J
Therefore, the difference in gravitational potential energy between points A and B is approximately 8,355.684 J.