Physics · Class 11 · Energy, Power, and Rotational Systems · Term 1

Work Done by a Constant Force

Students will define work and calculate work done by a constant force at various angles.

• CBSE Learning Outcomes
• CBSE: Work, Energy and Power - Class 11

About This Topic

Work done by a constant force is a fundamental concept in physics that helps students understand energy transfer. It is defined as the product of the force applied and the displacement in the direction of the force, given by W = F · d · cosθ, where θ is the angle between force and displacement vectors. This formula allows calculation of work in various scenarios, such as pushing a box horizontally or lifting an object vertically.

Students often explore positive work, when force and displacement align (cosθ > 0), negative work, as in friction opposing motion, and zero work, like when force is perpendicular to displacement, for example, centripetal force in circular motion. Key questions focus on how angle affects work and analysing no-work scenarios. Practical examples from everyday life, like pulling a rickshaw, make it relatable for Indian classrooms.

Active learning benefits this topic by letting students measure forces and displacements hands-on, which clarifies the role of angle and reinforces formula application through real experiments.

Key Questions

1. Explain how the angle between force and displacement affects the work done.
2. Differentiate between positive, negative, and zero work done by a force.
3. Analyze scenarios where a force is applied but no work is done on an object.

Learning Objectives

• Calculate the work done by a constant force acting at various angles to the displacement using the formula W = Fd cosθ.
• Classify work done as positive, negative, or zero based on the angle between the force and displacement vectors.
• Analyze specific scenarios to identify instances where a force is applied but no work is done.
• Compare the work done by a force when the angle of application changes, keeping force magnitude and displacement constant.

Before You Start

Vectors and Scalars

Why: Students need to understand the difference between vector and scalar quantities, and how to represent vectors, to grasp force and displacement as vectors.

Introduction to Force

Why: A basic understanding of what a force is and its units (Newtons) is necessary before calculating work done by a force.

Basic Trigonometry (Cosine Function)

Why: Students must be familiar with the cosine function to apply the W = Fd cosθ formula correctly.

Key Vocabulary

Work	In physics, work is done when a force causes an object to move over a distance. It is a measure of energy transfer.
Displacement	Displacement is the change in position of an object in a specific direction. It is a vector quantity.
Scalar Product (Dot Product)	The dot product of two vectors gives a scalar quantity. For work, it is the product of the magnitudes of force and displacement, and the cosine of the angle between them.
Perpendicular Force	A force that acts at a 90-degree angle to the direction of motion or displacement. Such a force does no work.

Watch Out for These Misconceptions

Common Misconception

Work is done whenever a force is applied, regardless of motion.

What to Teach Instead

Work requires displacement in the direction of the force's component; if there is no displacement or it is perpendicular, work is zero.

Common Misconception

Work is always positive if force causes motion.

What to Teach Instead

Work can be negative if force opposes displacement, like frictional force reducing kinetic energy.

Common Misconception

The magnitude of work depends only on force and distance, not angle.

What to Teach Instead

The angle between force and displacement determines the effective component, via cosθ.

Active Learning Ideas

Trolley Pull Experiment

Students use a trolley, weights, string, pulley, and protractor to apply force at different angles and measure displacement. They calculate work using W = F d cosθ and tabulate results. This helps visualise angle's effect.

25 min·Pairs

Force vs Displacement Graph

In pairs, students plot force-displacement data from pulling a block on a table. They shade areas to find work and compare with formula. Discusses constant force linearity.

20 min·Pairs

Zero Work Demo

Whole class observes a ball swung in vertical circle; mark tension perpendicular to motion. Calculate and confirm zero work by centripetal force.

15 min·Whole Class

Lifting vs Pushing

Individuals compare work in lifting a book vertically versus pushing horizontally same distance. Record observations and compute.

10 min·Individual

Real-World Connections

• Construction workers lifting heavy steel beams to build skyscrapers must calculate the work done against gravity. The angle at which the crane pulls the beam is crucial for efficiency.
• A farmer pulling a plough across a field does work. The angle of the pull relative to the ground affects the force needed and the actual work done in moving the soil.
• Sports scientists analyze the work done by athletes during training. For example, a weightlifter performing a clean and jerk does work against gravity, but the horizontal forces applied during the movement might do negligible work.

Assessment Ideas

Quick Check

Present students with three scenarios: (1) Pushing a box across a floor at an angle of 30 degrees. (2) Carrying a bag horizontally at a constant speed. (3) A car braking to a stop. Ask students to determine if work done is positive, negative, or zero in each case and briefly justify their answer.

Exit Ticket

Give students a problem: A force of 50 N is applied to an object, causing a displacement of 10 m. Calculate the work done if the angle between the force and displacement is 60 degrees. Then, ask them to explain in one sentence why a person holding a heavy object stationary does no work.

Discussion Prompt

Facilitate a class discussion using this prompt: 'Imagine you are pushing a stalled auto-rickshaw. How does the angle at which you push affect the work you do? What happens to the work done if the rickshaw starts moving in the direction you are pushing versus if you are pushing at an angle?'

Frequently Asked Questions

How does the angle between force and displacement affect work done?

The work done is W = F d cosθ. When θ = 0°, cosθ = 1, maximum positive work. At θ = 90°, cosθ = 0, zero work. For θ > 90°, cosθ negative, negative work. This shows only the component parallel to displacement contributes, vital for vector understanding in CBSE problems.

What is an example of zero work done by a force?

Consider a satellite in orbit; gravity provides centripetal force always perpendicular to velocity (displacement direction), so work by gravity is zero, conserving mechanical energy. In class, swinging a bucket of water demonstrates this with tension.

How does active learning benefit teaching work done by constant force?

Active learning engages students in experiments like pulling trolleys at angles, measuring real data, and calculating work. This builds intuition on cosθ effect, corrects misconceptions instantly through discussion, and links theory to practice, improving retention and CBSE exam performance over passive lectures.

Differentiate positive, negative, and zero work.

Positive work increases kinetic energy, force aids displacement (e.g., engine on car). Negative work decreases it, force opposes (friction). Zero work, no energy change (normal force on horizontal surface). Examples clarify in problems involving multiple forces.