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 effective weight of the cyclist?

Options:

Correct Answer: 60 kg

Solution:

Weight = Work / Height = 300 J / 5 m = 60 N; mass = Weight / g = 60 N / 9.8 m/s² ≈ 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 effective weight of the cyclist?

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

Step 1: Understand that work is done when a force moves an object over a distance. In this case, the cyclist does work to climb a hill.
Step 2: Identify the formula for weight based on work done and height. The formula is: Weight = Work / Height.
Step 3: Plug in the values from the question into the formula. Work = 300 J and Height = 5 m.
Step 4: Calculate the weight: Weight = 300 J / 5 m = 60 N.
Step 5: Understand that weight is related to mass by the formula: Weight = mass × g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 6: Rearrange the formula to find mass: mass = Weight / g.
Step 7: Plug in the weight you calculated (60 N) and the value of g (9.8 m/s²) into the formula: mass = 60 N / 9.8 m/s².
Step 8: Calculate the mass: mass ≈ 6.12 kg.

Work-Energy Principle – The work done on an object is equal to the change in its energy, which can be used to determine forces such as weight.
Weight Calculation – Weight is the force due to gravity acting on an object, calculated as mass times gravitational acceleration (W = mg).
Units of Measurement – Understanding the relationship between joules (work), meters (height), and newtons (weight) is crucial for solving physics problems.