Calculating Work Done in Lifting an Object: A Comprehensive Guide

How Much Work is Done When You Lift an Object that Weighs 150 N to the Height of 5 Meters?

Understanding the Concepts

When you lift an object, you are performing work. Work, in physics, is calculated as the force applied multiplied by the distance over which the force is applied. The formula is expressed as:

Work Force × Distance

Deconstructing the Calculations

In this scenario, the force is given as 150 N, and the distance is 5 meters. When calculating work, it's important to recognize that the force you apply (150 N) is typically only relevant in the context of lifting an object with a human. If the object is lifted using a machine, the effective force would be the weight of the object, which can be calculated as:

Weight (in Newtons) Mass (in kg) × Gravitational Acceleration (9.81 m/s2)

Given that the object weighs 150 N, we can find its mass:

Mass Weight / Gravitational Acceleration 150 N / 9.81 m/s2 ≈ 15.3 kg

Calculating Gravitational Potential Energy

When an object is lifted, it gains gravitational potential energy (GPE). The formula for GPE is:

GPE m × g × h

Where:

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

Substituting the given values:

GPE 15.3 kg × 9.81 m/s2 × 5 m ≈ 749.095 J

Breaking Down the Work Calculation

The total work done in lifting the object is the increase in its gravitational potential energy. However, the force used to lift the object (150 N) can also be considered. The work done by the person is calculated as:

Work Force × Distance

Work 150 N × 5 m 750 J

Therefore, the object gains approximately 749.095 J of gravitational potential energy, with a remaining 0.905 J due to the inaccuracy in the force application or other factors like friction. It's important to note that some of the work done will be converted into kinetic energy or heat, leading to the slight discrepancy.

Conclusion

In summary, the work done in lifting an object that weighs 150 N to a height of 5 meters is 750 J, and it results in a gain of 749.095 J in gravitational potential energy. This calculation helps us understand the physics behind lifting and the principles of work, force, and energy conversion. Understanding these concepts is crucial for a wide range of applications, from physics problems to real-world engineering tasks.