A girl with 50 kg mass climbs up a rope through a height of 5 metres. She takes 25 s to accomplish the task. What is the power (in watts) expended by the girl?
- AOption (a)
49
- BOption (b)
98
- COption (c)
68.6
- DOption (d)
88.2
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Correct answer
98
Why this answer is correct
The correct answer is Option 2: 98.
Key Points
- Work Done (W): The girl climbs up a rope through a height of 5 meters. The work done is calculated using the formula: Work Done (W) = m × g × h, where:
- m is the mass of the girl = 50 kg.
- g is the acceleration due to gravity = 9.8 m/s².
- h is the height climbed = 5 m.
Substituting the values: W = 50 × 9.8 × 5 = 2450 Joules.
- Power (P): Power is the rate at which work is done. It is calculated using the formula: P = W / t, where:
- W is the work done = 2450 Joules.
- t is the time taken = 25 seconds.
Substituting the values: P = 2450 / 25 = 98 Watts.
- Hence, the power expended by the girl is 98 Watts.
- The correct option is Option 2: 98.
Additional Information
- Work Done:
- Work is the transfer of energy that occurs when a force is applied to an object, causing displacement.
- Formula: W = F × d × cos(θ), where:
- F is the force applied.
- d is the displacement of the object.
- θ is the angle between the force and displacement.
- In this case, the force is due to gravity, so F = m × g.
- Power:
- Power is the rate at which work is done or energy is transferred.
- It is measured in Watts (W), where 1 Watt = 1 Joule/second.
- Formula: P = W / t, where:
- W is the work done.
- t is the time taken.
- Energy:
- Energy is the capacity to do work. It exists in various forms, such as potential energy, kinetic energy, and thermal energy.
- In this context, the girl gains gravitational potential energy as she climbs up the rope.
- Potential Energy (PE) = m × g × h, which is equivalent to the work done in lifting the girl.
- Acceleration Due to Gravity:
- The value of g is approximately 9.8 m/s² on the surface of the Earth.
- This value is used in calculations involving objects in free fall or being lifted vertically.
Important Points
- Units of Measurement:
- Work is measured in Joules (J).
- Power is measured in Watts (W).
- Force is measured in Newtons (N), where 1 Newton = 1 kg·m/s².
- Concept of Efficiency:
- The actual power expended may be higher due to inefficiencies such as friction or energy loss.
- In this problem, we assume ideal conditions with no energy losses.
- Practical Applications:
- Power calculations are crucial in understanding energy consumption in activities such as lifting, running, or operating machinery.
- It helps in designing efficient systems for energy use in various industries.