Calculating Gravitational Potential Energy: A Case Study of a Girl Running Up Stairs

Gravitational potential energy (P.E.) is a fundamental concept in physics that measures the energy gained by an object due to its position in a gravitational field. In the case of a girl who runs up a set of stairs, we can calculate the amount of gravitational potential energy she gains. This article will walk you through the process of calculating this energy using the given parameters and provide insights into the concept of potential energy.

Understanding the Problem

The problem statement describes a scenario where a girl weighing 400 Newtons (N) runs up a set of stairs that are 3 meters (m) high. The goal is to calculate the gravitational potential energy (P.E.) gained by the girl during this process.

The Formula for Gravitational Potential Energy

The formula for gravitational potential energy is:

P.E. mgh

Where:

m is the mass of the object g is the acceleration due to gravity (9.81 m/s2) h is the height of the object

Converting Weight to Mass

The weight of the girl is given as 400 Newtons. To find the mass, we can use the formula:

m W/g

Where:

Substituting the given values:

m 400 N / 9.81 m/s2 ≈ 40.8 kg

Calculating Gravitational Potential Energy

Now that we have the mass, we can calculate the gravitational potential energy using the formula P.E. mgh:

P.E. 40.8 kg * 9.81 m/s2 * 3 m

P.E. ≈ 1201.4 Joules

Thus, the girl gains approximately 1201.4 Joules of potential energy as she runs up the stairs.

Relevance of Time and Power

It is worth noting that the time it takes her (4 seconds) is actually irrelevant to finding the P.E., since potential energy only depends on the height and the mass of the object. However, it can be used to calculate the power, which is the rate of doing work. The power can be calculated as:

Power 1200 J / 4 s 300 Watts

While this calculation helps in understanding the rate at which the girl does work, it is not necessary for calculating the P.E. itself.

Additional Insights

The time it takes her to run up the stairs is a red herring. It distracts from the core concept, which is the calculation of gravitational potential energy.

Also, if you think you weigh more than this girl, you’re correct! This problem is designed to illustrate basic concepts, not to reflect real-life scenarios.

Understanding these principles will help you solve similar physics problems more efficiently. Gravitational potential energy is a key concept in physics and is widely applicable in various real-world scenarios.