Work-Energy Theorem - UNSOLVED PRACTICE SET

Q7. State the work-energy theorem for a constant force. Write the mathematical expression.

Q8. Prove the work-energy theorem for a constant force acting on a body moving on a frictionless horizontal surface

Q9. A bullet of mass 20 g moving at 400 m/s penetrates a wooden block and comes to rest. Calculate the work done by the block on the bullet.

Q10. In your school playground, a 500 g cricket ball is thrown vertically upward with a speed of 20 m/s. Using the work-energy theorem, calculate the maximum height reached. (Take g = 10 m/s²)

Q11. A car of mass 1000 kg moving at 72 km/h is brought to rest by brakes. Calculate the work done by the braking force.

Q12. How does the work-energy theorem explain that the work done by all forces (including non-conservative forces) equals the change in kinetic energy?

Q13. State and prove the work-energy theorem for:

(i) A constant force

(ii) A variable force

Discuss the significance of this theorem and why it is considered one of the most powerful tools in mechanics.

Q14. A body of mass 5 kg is initially at rest on a rough horizontal surface (μ = 0.2). A horizontal force of 30 N acts on it through a distance of 10 m.

(a) Calculate the work done by the applied force.

(b) Calculate the work done by friction.

(c) Calculate the net work done on the body.

(d) Using the work-energy theorem, find the final velocity of the body.

(e) Verify your answer using Newton's second law and kinematic equations.

Q15. A block of mass 2 kg is released from rest at the top of a frictionless incline of height 5 m and length 13 m.

(a) Calculate the work done by gravity as the block slides down.

(b) Calculate the work done by the normal reaction.

(c) Using the work-energy theorem, find the speed of the block at the bottom.

(d) If the incline were rough (μ = 0.3), recalculate the speed at the bottom using the work-energy theorem.

(e) Compare the two cases and discuss the role of non-conservative forces.

Q16. A 50 kg skater starts from rest and slides down a frictionless hemispherical ice bowl of radius 10 m.

(a) Calculate the speed of the skater at the bottom using the work-energy theorem.

(b) Calculate the normal reaction on the skater at the bottom.

(c) If the skater continues and slides up the other side, to what height will she rise?

(d) What happens if there is friction (μ = 0.1) on the horizontal part at the bottom?

(e) Calculate the distance travelled on the rough horizontal part before stopping.

Q17. A 0.5 kg block attached to a spring (k = 200 N/m) is displaced 10 cm from its equilibrium position on a frictionless surface and released.

(a) Calculate the initial potential energy stored in the spring.

(b) Using the work-energy theorem, find the speed of the block as it passes through the equilibrium position.

(c) Calculate the kinetic energy when the block is at x = 5 cm.

(d) At what position is the kinetic energy equal to the potential energy?

(e) Sketch the graphs of kinetic energy, potential energy, and total energy vs position.

Q18. In a school experiment, a trolley of mass 1 kg is pulled by a hanging mass of 0.5 kg through a distance of 1 m on a frictionless track.

(a) Draw the free body diagrams for both masses.

(b) Calculate the work done by gravity on the falling mass.

(c) Using the work-energy theorem for the system, calculate the velocity of the trolley after moving 1 m.

(d) Calculate the tension in the string using the work-energy approach.

(e) Verify your result using Newton's second law.