In one day, a 75-kg mountain climber ascends from the 1500-m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1350 m. What is her change in gravitational potential energy (a) on the first day?

Verified step by step guidance

1. Identify the mass of the climber, which is given as 75 kg.
2. Calculate the change in height on the first day by subtracting the initial elevation from the final elevation. Initial elevation is 1500 m and final elevation is 2400 m.
3. Use the formula for gravitational potential energy, which is \( \Delta U = mgh \), where \( m \) is mass, \( g \) is the acceleration due to gravity (approximately 9.8 m/s^2), and \( h \) is the change in height.
4. Substitute the values into the formula: \( m = 75 \) kg, \( g = 9.8 \) m/s^2, and \( h \) is the result from step 2.
5. Calculate the change in gravitational potential energy (\( \Delta U \)) using the values substituted in the formula.

Key Concepts

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height above a reference point. In this scenario, the climber's change in height will directly affect her GPE.

Change in Height

The change in height (Δh) is a critical factor in determining the change in gravitational potential energy. It is calculated by subtracting the initial height from the final height. In the given problem, the climber ascends from 1500 m to 2400 m, resulting in a positive change in height, which will increase her gravitational potential energy.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms (kg). Weight, on the other hand, is the force exerted by gravity on that mass, calculated as weight = mass × gravity (W = mg). In this question, the climber's mass of 75 kg is essential for calculating the change in gravitational potential energy as she ascends the cliff.