Understanding Work Done in Physics: A Case Study of a Person and a Bucket

Introduction

When we talk about work done in physics, the concept can often be confusing. This article aims to clarify the scenario where a person holds a bucket and moves it through different paths. We will delve into the specifics of work done in both horizontal and vertical directions to ensure a comprehensive understanding.

Defining Work in Physics

In physics, work is defined as the product of force and displacement in the direction of the force. The mathematical expression for work is:

[ text{Work} text{Force} times text{Distance} times cos(theta) ]

Where:

( text{Force} ) ( text{Distance} ) ( theta ) is the angle between the force and the direction of motion

Horizontal Movement

The person walks 7 meters horizontally while holding the bucket. Given that the weight of the bucket (60 N) acts vertically, the angle between the vertical force and the horizontal direction is 90 degrees. Since the work done is zero when the force and displacement are perpendicular, we can calculate the work done in this case:

[ text{Work}_{text{horizontal}} 60 , text{N} times 7 , text{m} times cos(90^circ) 0 , text{J} ]

Hence, no work is done in the horizontal direction.

Vertical Movement

The person then climbs up a vertical distance of 5 meters. In this scenario, the work done against the gravitational force needs to be calculated:

[ text{Work}_{text{vertical}} -text{Weight} times text{Height} -60 , text{N} times 5 , text{m} -300 , text{J} ]

The negative sign indicates that the work is done against the gravitational force. Here, the force (60 N) and the displacement (5 m) are both positive, but the direction of the force is opposite to the displacement, hence the negative sign.

Summary and Total Work Done

Combining the work done in both directions, we get:

[ text{Total Work} text{Work}_{text{horizontal}} text{Work}_{text{vertical}} 0 , text{J} - 300 , text{J} -300 , text{J} ]

Therefore, the total work done by the person is -300 J.

Conclusion and Clarification

It is important to understand that the work done against gravity involves a consideration of the direction of the force. In this case, since the force due to gravity acts downward and the displacement is upward, the work done is negative. Conversely, if the force and displacement were in the same direction, the work done would be positive.

Frequently Asked Questions (FAQs)

Q: Why is the work done in the horizontal direction 0 J?
A: The work done in the horizontal direction is zero because the force (weight) and the displacement are perpendicular to each other. Q: Why is the work done in the vertical direction negative?
A: The work done is negative because the force due to gravity and the displacement are in opposite directions. Q: Can the work done be positive in this scenario?
A: If the person was lowering the bucket under the influence of gravity, the work done would be positive.

References

Physics textbooks on work and energy Online physics resources and forums