A person lifts a piece of luggage of mass 20 kg from the ground and places it on his head at a height of 2 m above the ground. Taking g = 10 m/s^2, what is the work done by him against gravity?

Introduction / Context:
Work, energy and power are core topics in mechanics. In everyday life, lifting a suitcase or a bucket of water seems like a simple action, but in physics it directly illustrates the concept of work done against gravitational force. Whenever a person raises an object vertically, they increase its gravitational potential energy. This question asks you to calculate the work done by a person when lifting a 20 kg piece of luggage from the ground to a height of 2 m on his head, using a rounded value for the acceleration due to gravity. It is a standard example of work done in raising a body to a certain height.

Given Data / Assumptions:
• Mass of the luggage, m = 20 kg. • Vertical height raised, h = 2 m above the ground. • Acceleration due to gravity, g = 10 m/s^2 (approximate value). • The luggage is lifted slowly so that its kinetic energy change is negligible and motion is vertical. • Air resistance and other small losses are ignored, so work done equals gain in gravitational potential energy.

Concept / Approach:
In mechanics, the work W done against gravity in lifting a body of mass m through a vertical height h is equal to the increase in gravitational potential energy and is given by the formula W = m * g * h. This is because the gravitational force acting downward on the object has magnitude m * g, and moving the object upward through distance h against this force requires doing positive work. By substituting the given mass, gravitational acceleration, and height into this formula, we can directly compute the work done in joules. This approach is a straightforward application of the definition of work done by a constant force.

Step-by-Step Solution:
Step 1: Write the formula for work done against gravity when lifting an object vertically: W = m * g * h. Step 2: Substitute the given mass m = 20 kg into the formula. Step 3: Substitute the given acceleration due to gravity g = 10 m/s^2. Step 4: Substitute the given height h = 2 m. Step 5: Calculate W = 20 * 10 * 2 = 400 joules. Step 6: Conclude that the person does 400 J of work against gravity in lifting the luggage to his head.

Verification / Alternative check:
To check the calculation, you can first calculate the weight of the luggage. The weight is the gravitational force F = m * g = 20 * 10 = 200 newtons. Then, use the work formula W = F * s, where s is the displacement in the direction of the force. Here, the force that must be overcome is 200 newtons, and the displacement is 2 m upward. So W = 200 * 2 = 400 joules, which matches the earlier result. This confirms that 400 J is consistent whether you use the potential energy method or the direct force displacement approach.

Why Other Options Are Wrong:
Option A, 20 J, is far too small because it effectively uses only the mass without multiplying by g and height. Option C, 200 J, corresponds to using either half of the correct height or forgetting one factor of 2 when multiplying. Option D, 40 J, is also much too small and may come from confusing kilograms with newtons. None of these incorrect options satisfy the correct formula W = m * g * h with the given values of mass, gravity, and height.

Common Pitfalls:
A common mistake is to forget to convert mass into force by multiplying by g, leading students to use W = m * h instead of W = m * g * h. Another error is mixing units such as treating kilograms as newtons directly. Some learners also confuse work with power and attempt to include time, which is unnecessary unless the rate of doing work is being asked. Always remember that for vertical lifting in a uniform gravitational field, the work done against gravity depends only on the mass, gravitational acceleration, and vertical height raised.

Final Answer:
The correct choice is 400 J, because the work done against gravity in lifting the 20 kg luggage through a vertical height of 2 m with g = 10 m/s^2 is W = 20 * 10 * 2 = 400 joules.