What is the Relation between Work, Force & Displacement? | Simple Explanation for Class 10

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What is the Relation between Work, Force and Displacement?

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Work, force, and displacement are related by a simple formula: Work done is equal to the force applied multiplied by the displacement in the direction of the force. This means that for work to be done, a force must cause an object to move some distance.

Simple Example

Quick Example

Imagine pushing your school bag across the classroom floor. If you push with a certain force and the bag moves 2 meters, you have done work. If you push with the same force but the bag doesn't move at all, no work is done, even though you applied force.

Worked Example

Step-by-Step

PROBLEM: A delivery person pushes a package with a force of 50 Newtons (N) over a distance of 10 meters (m) to load it onto a truck. How much work is done?
---STEP 1: Identify the given values.
Force (F) = 50 N
Displacement (d) = 10 m
---STEP 2: Recall the formula for work.
Work (W) = Force (F) x Displacement (d)
---STEP 3: Substitute the values into the formula.
W = 50 N x 10 m
---STEP 4: Calculate the work done.
W = 500 Joules (J)
---ANSWER: The work done is 500 Joules.

Why It Matters

Understanding this relationship is crucial for engineers designing anything from robots to rockets, ensuring maximum efficiency. It's also vital in medicine for designing prosthetics or understanding muscle movement, and in AI for teaching machines how to interact with the physical world. Many careers, like mechanical engineering, sports science, and robotics, rely on these concepts daily.

Common Mistakes

MISTAKE: Thinking work is done if force is applied, even if there's no movement. | CORRECTION: Work is only done if the force causes a displacement. If you push a wall and it doesn't move, zero work is done, even if you feel tired.

MISTAKE: Forgetting that displacement must be in the direction of the force. | CORRECTION: If you carry a heavy bucket of water horizontally (walking forward), the force you apply is upwards (against gravity), but your displacement is horizontal. In this case, no work is done by the upward force in the direction of your movement.

MISTAKE: Confusing the units of force, work, and displacement. | CORRECTION: Force is measured in Newtons (N), displacement in meters (m), and work in Joules (J). Remember: 1 Joule = 1 Newton-meter.

Practice Questions

Try It Yourself

QUESTION: How much work is done if a boy pulls a toy car with a force of 20 N for a distance of 5 m? | ANSWER: 100 J

QUESTION: A coolie lifts a suitcase weighing 150 N from the ground to a height of 1.5 m. Calculate the work done by the coolie. | ANSWER: 225 J

QUESTION: A force of 10 N acts on an object, but it only moves 200 cm. What is the work done? (Hint: Watch your units!) | ANSWER: 20 J

MCQ

Quick Quiz

Which of the following scenarios results in zero work done?

A student pushes a desk 2 meters across the room.

A person lifts a 5 kg bag from the floor to a table.

A car engine applies force, but the car is stuck in mud and doesn't move.

A child pulls a wagon up a small hill.

The Correct Answer Is:

Work requires both force and displacement. In option C, force is applied by the engine, but there is no displacement (the car doesn't move), so no work is done.

Real World Connection

In the Real World

When you use a hand pump to draw water from a well in a village, you apply a force downwards on the handle, and the water is displaced upwards. The work you do on the handle is transferred to lift the water. Similarly, when a crane at a construction site lifts heavy steel beams, it's doing significant work, calculated by the force it applies and the height the beam is lifted.

Key Vocabulary

Key Terms

WORK: The energy transferred when a force causes an object to move | FORCE: A push or a pull that can change an object's motion | DISPLACEMENT: The change in position of an object in a specific direction | JOULE: The SI unit of work and energy | NEWTON: The SI unit of force

What's Next

What to Learn Next

Next, you can explore different types of energy, such as kinetic and potential energy, and how they relate to the work done. Understanding work is a crucial step towards grasping the Law of Conservation of Energy, which is fundamental to all of physics!