A girl of weight 440 N climbs up a rope through a height of 7 m in 20 s. The power expended by the girl is:
154 W
Understanding Power Expended in Climbing
This physics problem asks us to calculate the power expended by a girl climbing a rope. Power is the rate at which work is done. In this case, the work done is against the force of gravity as the girl increases her height.
Identifying Given Information
We are given the following information:
- Weight of the girl (which is the force she exerts against gravity): \(F = 440 \text{ N}\)
- Height climbed (the distance): \(d = 7 \text{ m}\)
- Time taken to climb: \(t = 20 \text{ s}\)
Calculating Work Done Against Gravity
The work done (\(W\)) when moving against a constant force over a distance is given by the formula:
\[W = \text{Force} \times \text{Distance}\]
In this scenario, the force is the girl's weight, and the distance is the height she climbs. So, the work done is:
\[W = F \times d\]
Substituting the given values:
\[W = 440 \text{ N} \times 7 \text{ m}\]
\[W = 3080 \text{ Joules}\]
The work done by the girl in climbing the rope is 3080 Joules.
Calculating Power Expended
Power (\(P\)) is the rate at which work is done. It is calculated using the formula:
\[P = \frac{\text{Work done}}{\text{Time taken}}\]
Using the work done we just calculated and the time taken:
\[P = \frac{W}{t}\]
Substituting the values:
\[P = \frac{3080 \text{ J}}{20 \text{ s}}\]
\[P = 154 \text{ J/s}\]
Since 1 Joule per second is equal to 1 Watt (W), the power expended by the girl is:
\[P = 154 \text{ W}\]
Final Power Calculation
The power expended by the girl climbing the rope is 154 W.
Revision Table: Work, Energy, and Power Concepts
| Concept | Definition | Formula | SI Unit |
|---|---|---|---|
| Work (W) | Energy transferred by a force acting over a distance. | \(W = F \times d \times \cos(\theta)\) (where \(\theta\) is angle between force and displacement) | Joule (J) |
| Potential Energy (Gravitational) (PE) | Energy stored by an object due to its position in a gravitational field. | \(PE = mgh\) or \(PE = \text{weight} \times \text{height}\) | Joule (J) |
| Power (P) | The rate at which work is done or energy is transferred. | \(P = \frac{W}{t}\) or \(P = F \times v\) (where v is velocity) | Watt (W) |
Additional Information: Climbing and Power
When a person climbs vertically, they are doing work against gravity. The force they exert is equal to their weight (assuming constant velocity or average power). The work done results in an increase in the person's gravitational potential energy. The power calculated here represents the useful power output against gravity. The total power generated by the girl would be higher, including power expended against air resistance and internal biological inefficiencies.
The unit of power, the Watt (W), is named after James Watt, a Scottish inventor, mechanical engineer, and chemist.
Similar Questions
"Pathfinder", an American Spacecraft, landed on the planet _______ in 1997.
- A/an ______ circle is a circular centre line on a drawing containing the centres of holes about a common centre.
- Which of the following is an example of a third-class lever?
_______ is the distance from the pitch circle to the bottom of the tooth space in a gear.
In a Class 3 lever, the effort and load move:
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A mass is attached to a spring that hangs vertically. The extension produced in the spring is 6 cm on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be:
Directions: Each item in this section consists of a sentence with an underlined word followed by four words (a), (b), (c), and (d). Select the option that is opposite in meaning to the underlined word and mark your response in your Answer Sheet accordingly.
The deluge affected the population.The major source of vitamins and minerals for vegetarians is
Which of the following statements about the Deccan Riots Commission is/are correct?
1. The Commission did not hold enquiries in the districts which were not affected.
2. The Commission did record the statements of ryots, sahukars and eye-witnesses.
Select the correct answer using the code given below:
