Calculating the Work Done by a Climbing Man: A Physics Problem

In physics, one common scenario involves calculating the work done by a person climbing a staircase. This problem can be solved using the principle of gravitational potential energy, and the formula Work mgh. This article will guide you through the process of calculating the work done by a man of mass 60 kg who climbs up a 20 m long staircase to the top of a building that’s 10 m high. We will also explore the related concepts of energy and power.

Understanding the Problem

Consider a man of mass 60 kg climbing a staircase that is 20 m long to reach the top of a building 10 m high. The acceleration due to gravity, denoted by g, is given as 10 m/s2. The relevant formula to calculate the work done by the man is:

Work m × g × h

Step-by-Step Calculation

Let’s substitute the values into the formula to find out the work done:

Work 60 kg × 10 m/s2 × 10 m 6000 Joules

Concepts Involved

1. Gravitational Potential Energy (GPE) This is the energy possessed by an object due to its position in a gravitational field. The formula for GPE is E mgh, where: m is the mass of the object, g is the acceleration due to gravity, h is the height climbed (in this case, 10 m). 2. Energy Energy is the capacity to do work, and in this context, the work performed by the man. The energy gained is equal to the work done by the man, which is 6000 Joules. 3. Power Power is the rate at which work is done and is given by the formula Power Work / Time. If the man runs up the stairs in 5 seconds: Power 6000 Joules / 5 seconds 1200 Watts If the man walks up the stairs in 30 seconds: Power 6000 Joules / 30 seconds 200 Watts

Practice and Application

This problem is a simple but fundamental example in physics. It helps one understand the relationship between mass, height, and the work done against gravity. Such problems are often used to reinforce the principles of energy conservation and the practical applications of physics in everyday scenarios.

Conclusion

The work done by the man in climbing the stairs is 6000 Joules. This problem involves understanding and applying the concept of gravitational potential energy, which is a crucial aspect of physics. By breaking down the problem into smaller, manageable steps, we can understand and solve complex physics problems more effectively.