Work Done by a Variable Force

Oct 13, 2025 by wbrum.org 83 views

Introduction

In physics, work is a measure of the energy transferred by a force to an object as it moves. It is a fundamental concept in mechanics and is used to describe the interaction between a system and its environment. In this article, we will explore the concept of work done by a force and provide a step-by-step solution to a problem involving an object of mass 20 kg moving at a speed of 2 m/s, acted upon by a force for 2 s and achieving a velocity of 8 m/s.

What is Work?

Work is defined as the product of the force applied to an object and the distance over which the force is applied. Mathematically, it can be represented as:

W = F × d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

Work Done by a Variable Force

However, in many real-world scenarios, the force applied is not constant, and the distance over which the force is applied is not fixed. In such cases, the work done by the force can be calculated using the following formula:

W = ∫F(x) dx

where W is the work done, F(x) is the force applied as a function of distance x, and dx is the infinitesimal distance element.

Problem Statement

An object of mass 20 kg is moving at a speed of 2 m/s. It is acted upon by a force for 2 s and achieves a velocity of 8 m/s. Find the work done by the force.

Step 1: Calculate the Acceleration

To find the work done by the force, we need to calculate the acceleration of the object. We can use the following formula:

a = Δv / Δt

where a is the acceleration, Δv is the change in velocity, and Δt is the time over which the force is applied.

Δv = v_f - v_i = 8 m/s - 2 m/s = 6 m/s

Δt = 2 s

a = 6 m/s / 2 s = 3 m/s^2

Step 2: Calculate the Force

We can use Newton's second law of motion to calculate the force applied to the object:

F = m × a

where F is the force, m is the mass of the object, and a is the acceleration.

m = 20 kg

a = 3 m/s^2

F = 20 kg × 3 m/s^2 = 60 N

Step 3: Calculate the Work Done

Now that we have the force and the distance over which the force is applied, we can calculate the work done by the force:

W = F × d

However, we need to find the distance over which the force is applied. We can use the following formula:

d = v_i × Δt + (1/2) × a × Δt^2

where d is the distance, v_i is the initial velocity, Δt is the time over which the force is applied, and a is the acceleration.

v_i = 2 m/s

Δt = 2 s

a = 3 m/s^2

d = 2 m/s × 2 s + (1/2) × 3 m/s^2 × (2 s)^2 = 4 m + 6 m = 10 m

W = F × d = 60 N × 10 m = 600 J

Conclusion

In this article, we explored the concept of work done by a force and provided a step-by-step solution to a problem involving an object of mass 20 kg moving at a speed of 2 m/s, acted upon by a force for 2 s and achieving a velocity of 8 m/s. We calculated the acceleration, force, and work done by the force using the formulas of physics. The work done by the force was found to be 600 J.

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Introduction

In our previous article, we explored the concept of work done by a force and provided a step-by-step solution to a problem involving an object of mass 20 kg moving at a speed of 2 m/s, acted upon by a force for 2 s and achieving a velocity of 8 m/s. In this article, we will answer some frequently asked questions related to work done by a force.

Q: What is the difference between work and energy?

A: Work and energy are related but distinct concepts in physics. Work is the transfer of energy from one object to another through a force, while energy is the ability to do work. In other words, work is a measure of the energy transferred, while energy is the capacity to perform work.

Q: Can work be negative?

A: Yes, work can be negative. When a force is applied in the opposite direction of the motion of an object, the work done is negative. This is because the force is opposing the motion, and therefore, the energy is being transferred from the object to the environment.

Q: What is the unit of work?

A: The unit of work is the joule (J). It is defined as the energy transferred when a force of 1 newton (N) is applied over a distance of 1 meter (m).

Q: Can work be done by a force on an object that is not moving?

A: Yes, work can be done by a force on an object that is not moving. For example, when a force is applied to a stationary object, the work done is zero, but the force is still doing work on the object. This is because the force is transferring energy to the object, even though the object is not moving.

Q: What is the relationship between work and kinetic energy?

A: The work done by a force on an object is equal to the change in its kinetic energy. This is because the force is transferring energy to the object, which is then converted into kinetic energy.

Q: Can work be done by a force on an object that is moving in a circular path?

A: Yes, work can be done by a force on an object that is moving in a circular path. For example, when a force is applied to a car moving in a circular path, the work done is zero, but the force is still doing work on the car. This is because the force is transferring energy to the car, even though the car is not moving in a straight line.

Q: What is the significance of work in real-world applications?

A: Work is a fundamental concept in many real-world applications, including engineering, physics, and chemistry. It is used to describe the interaction between a system and its environment, and it is essential in understanding the behavior of objects in various situations.

Q: Can work be done by a force on an object that is moving in a non-uniform motion?

A: Yes, work can be done by a force on an object that is moving in a non-uniform motion. For example, when a force is applied to a car moving in a non-uniform motion, the work done is equal to the change in its kinetic energy.

Conclusion

In this article, we answered some frequently asked questions related to work done by a force. We discussed the difference between work and energy, the unit of work, and the relationship between work and kinetic energy. We also explored the significance of work in real-world applications and its relationship with non-uniform motion.

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.