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 them.
The formula for gravitational potential energy is given by:
PE = mgh
Where:
PE = gravitational potential energy
m = mass of the skier (52 kg)
g = acceleration due to gravity (9.81 m/s²)
h = height
First, let's calculate the potential energy at point A.
PE_A = m * g * h_A
Given that the skier is 17.7 m vertically above point B, the height at point A (h_A) is 17.7 m.
Now, let's calculate the potential energy at point B.
PE_B = m * g * h_B
Since the zero level for gravitational potential energy is at point B, the height at point B (h_B) would be zero.
Now, we can find the difference in gravitational potential energy:
ΔPE = PE_A - PE_B
Substituting the values we have:
ΔPE = (m * g * h_A) - (m * g * h_B)
ΔPE = m * g * (h_A - h_B)
Substituting the given values:
ΔPE = 52 kg * 9.81 m/s² * (17.7 m - 0)
Calculating the expression:
ΔPE = 52 kg * 9.81 m/s² * 17.7 m
ΔPE ≈ 9,359.604 J
Therefore, the difference in gravitational potential energy associated with the skier at points A and B is approximately 9,360 J.