medium difficulty5 min

Positive, Negative, and Zero Work

The sign of work depends on the angle between force and displacement: work is positive when both are in the same direction, negative when opposite, and zero when perpendicular or when displacement is absent.

In one line: Same helps, opposite resists, perpendicular does no work.

Practice This Concept

Understand it

Positive work increases or supports motion, like gravity doing work on a falling stone. Negative work opposes motion, like friction on a sliding box. Zero work occurs when force does not produce displacement in its direction, such as centripetal force in uniform circular motion at an instant.

Example

When a ball moves upward, gravity acts downward, so work done by gravity is negative.

Rule to remember

Using W = F·s·cosθ: θ = 0° gives positive work, θ = 180° gives negative work, and θ = 90° gives zero work.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1A 10 N frictional force opposes a box moving 2 m.
2Work by friction = -10 × 2 = -20 J because force is opposite to displacement.

Method you can reuse

Mark displacement direction, mark force direction, compare the angle, assign the sign, then calculate if values are given.

Sketch it in your answer

Use three small cases with arrows: force parallel to displacement, force opposite to displacement, and force perpendicular to displacement.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is the work done by friction on a sliding book negative?

Think first, then show answer

The work done by friction is negative because friction acts opposite to the displacement of the sliding book.

Common wrong answer

Calling frictional work positive.

Why it loses marks: Friction usually acts opposite to displacement.

Don't mix this up

Students often say work is negative only when the object moves backward, but it actually depends on force direction relative to displacement.

Exam tip

Draw force and displacement arrows. Same direction gives positive work, opposite direction gives negative work, and perpendicular gives zero work.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Exams ask for examples of positive, negative, and zero work, or ask students to identify the sign from a situation.

1
Enough for 1 mark
The sign of work depends on the angle between force and displacement: work is positive when both are in the same direction, negative when opposite, and zero when perpendicular or when displacement is absent.
2
Add for 2 marks
Example: When a ball moves upward, gravity acts downward, so work done by gravity is negative.
3
Add for 3 marks
Positive work increases or supports motion, like gravity doing work on a falling stone.

MCQ Quiz

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