Work done by a force at an angle: Class 9 practice
Only the part of the force along the displacement does work: W = Fs cos θ. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Cosine values
The idea behind work done by a force at an angle
Only the part of the force along the displacement does work: W = Fs cos θ. At 90° no work is done; when force opposes motion (θ = 180°) work is negative.
Step-by-step method
- Find the angle between force and displacement.
- W = Fs cos θ.
- Check the sign.
Worked example 1 (Basic)
A 35 N force moves an object 16 m. The force is at 0° to the motion. Find the work done.
- W = 35 × 16 × cos 0°
- = 560 J
- Answer: 560 J
Worked example 2 (Standard)
A 60 N force moves an object 9 m. The force is at 30° to the motion. Find the work done.
- W = 60 × 9 × cos 30°
- = 467.65 J
- Answer: 467.65 J
Worked example 3 (Challenge)
A 64 N force moves an object 17 m. The force is at 120° to the motion. Find the work done.
- W = 64 × 17 × cos 120°
- = -544 J
- Answer: -544 J
Common mistakes and misconceptions
- Using F × s when the force is at an angle
- Saying work is done when carrying a bag horizontally
Practice questions
- (Basic) A 55 N force moves an object 2 m. The force is at 0° to the motion. Find the work done.
- (Basic) A 24 N force moves an object 1 m. The force is at 0° to the motion. Find the work done.
- (Standard) A 60 N force moves an object 20 m. The force is at 30° to the motion. Find the work done.
- (Standard) A 52 N force moves an object 17 m. The force is at 60° to the motion. Find the work done.
- (Challenge) A 94 N force moves an object 20 m. The force is at 120° to the motion. Find the work done.
- (Challenge) A 98 N force moves an object 2 m. The force is at 180° to the motion. Find the work done.
Answer key with full working
- Q1: W = 55 × 2 × cos 0° → = 110 J → Answer: 110 J
- Q2: W = 24 × 1 × cos 0° → = 24 J → Answer: 24 J
- Q3: W = 60 × 20 × cos 30° → = 1039.23 J → Answer: 1039.23 J
- Q4: W = 52 × 17 × cos 60° → = 442 J → Answer: 442 J
- Q5: W = 94 × 20 × cos 120° → = -940 J → Answer: -940 J
- Q6: W = 98 × 2 × cos 180° → = -196 J → Answer: -196 J
Syllabus note
This skill is listed under "Work and Energy" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is work done by a force at an angle in?
"Work and Energy", Class 9 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.