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 consider the change in height (vertical distance) and the mass of the skier.
The formula for calculating the gravitational potential energy is:
PE = m * g * h
where PE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the vertical height.
Let's calculate the gravitational potential energy at point A:
PE_A = m * g * h_A
Given:
m = 52 kg
g = 9.81 m/s^2
h_A = 17.7 m (vertical height at point A)
Substituting the given values into the formula:
PE_A = 52 * 9.81 * 17.7
Now let's calculate the gravitational potential energy at point B:
PE_B = m * g * h_B
Given:
h_B = 0 m (as the zero level for gravitational potential energy is at point B)
Substituting the given values:
PE_B = 52 * 9.81 * 0
Since the height at point A is greater than at point B, the difference in gravitational potential energy can be calculated as:
ΔPE = PE_A - PE_B
Substituting the calculated values into the formula:
ΔPE = (52 * 9.81 * 17.7) - (52 * 9.81 * 0)
Now we can perform the calculation:
ΔPE = 52 * 9.81 * 17.7
Calculating the value:
ΔPE ≈ 9,131.852 J
Therefore, the difference in gravitational potential energy associated with the skier at points A and B, with the zero level at point B, is approximately 9,131.852 J.