Open Question
(I) By how much does the gravitational potential energy of a 58-kg pole vaulter change if her center of mass rises 4.0 m during the jump?
10. Conservation of Energy
Gravitational Potential Energy
Multiple Choice
A car is driving up a hill. What is the change in potential energy of the car when it undergoes a displacement of .
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Verified step by step guidance1
Identify the relevant components of the displacement vector. The displacement vector is given as \( \mathbf{d} = (210\, \text{m})\hat{i} + (2.0\, \text{m})\hat{j} \). The vertical component, \( (2.0\, \text{m})\hat{j} \), is relevant for calculating the change in potential energy.
Recall the formula for gravitational potential energy: \( \Delta U = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the change in height.
Substitute the known values into the formula. Here, \( m = 500\, \text{kg} \), \( g = 9.8\, \text{m/s}^2 \), and \( h = 2.0\, \text{m} \).
Calculate the change in potential energy using the formula: \( \Delta U = 500\, \text{kg} \times 9.8\, \text{m/s}^2 \times 2.0\, \text{m} \).
Convert the result from joules to kilojoules by dividing by 1000, since 1 kJ = 1000 J.
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