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

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Question: A cyclist does 300 J of work to climb a hill. If the hill is 5 m high, what is the weight of the cyclist? (2020)

Options:

Correct Answer: 60 kg

Exam Year: 2020

Solution:

Work = m × g × h. 300 J = m × 9.8 m/s² × 5 m. m = 300 J / (9.8 m/s² × 5 m) = 6.12 kg.

A cyclist does 300 J of work to climb a hill. If the hill is 5 m high, what is the weight of the cyclist? (2020)

A cyclist does 300 J of work to climb a hill. If the hill is 5 m high, what is the weight of the cyclist? (2020)

Step 1: Understand that work done (W) is equal to the weight of the cyclist (m × g) multiplied by the height of the hill (h). The formula is W = m × g × h.
Step 2: Identify the values given in the problem: Work (W) = 300 J, height (h) = 5 m, and the acceleration due to gravity (g) = 9.8 m/s².
Step 3: Substitute the known values into the formula: 300 J = m × 9.8 m/s² × 5 m.
Step 4: Simplify the equation: 300 J = m × 49 m/s² (since 9.8 m/s² × 5 m = 49 m/s²).
Step 5: To find the mass (m), rearrange the equation: m = 300 J / 49 m/s².
Step 6: Calculate the value: m = 300 / 49, which equals approximately 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 in this case relates to gravitational potential energy.
Gravitational Force – Understanding the relationship between mass, gravitational acceleration, and weight is crucial for solving problems involving forces acting on objects.
Units of Measurement – Recognizing and correctly using units such as Joules (J), meters (m), and kilograms (kg) is essential for accurate calculations.