A cyclist does 300 J of work to climb a hill. If the height of the hill is 5 m,

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Question: A cyclist does 300 J of work to climb a hill. If the height of the hill is 5 m, what is the mass of the cyclist? (g = 9.8 m/s²)

Options:

Correct Answer: 6.12 kg

Solution:

Using Work = mgh; m = Work / (gh) = 300 J / (9.8 m/s² * 5 m) = 6.12 kg.

A cyclist does 300 J of work to climb a hill. If the height of the hill is 5 m, what is the mass of the cyclist? (g = 9.8 m/s²)

A cyclist does 300 J of work to climb a hill. If the height of the hill is 5 m, what is the mass of the cyclist? (g = 9.8 m/s²)

Step 1: Understand the formula for work done against gravity, which is Work = mgh, where m is mass, g is the acceleration due to gravity, and h is height.
Step 2: Identify the values given in the problem: Work = 300 J, g = 9.8 m/s², and h = 5 m.
Step 3: Rearrange the formula to solve for mass (m): m = Work / (gh).
Step 4: Substitute the values into the formula: m = 300 J / (9.8 m/s² * 5 m).
Step 5: Calculate the denominator: 9.8 m/s² * 5 m = 49 m²/s².
Step 6: Divide the work by the calculated value: m = 300 J / 49 m²/s².
Step 7: Perform the division: m ≈ 6.12 kg.

Work-Energy Principle – This principle states that the work done on an object is equal to the change in its energy, which can be applied to calculate mass when given work and height.
Gravitational Potential Energy – This concept relates to the energy an object possesses due to its position in a gravitational field, calculated as mgh.