Potential Energy - UNSOLVED PRACTICE SET

Q7. Define gravitational potential energy. Write its formula and explain what happens to it when an object is lifted higher.

Q8. What is elastic potential energy? Give two examples from everyday Indian life where elastic PE is stored and then used.

Q9. A water tank is built on the rooftop of a school at a height of 12 m. The water stored has a mass of 500 kg. Calculate the gravitational PE of the water. (g = 10 m/s²) Why is this height important for water supply?

Q10. The reference level for gravitational PE can be chosen freely. Explain what this means and why the change in PE (ΔPE = mgΔh) is more meaningful than the absolute PE value.

Q11. A diver stands on a 10 m high diving board. Compare her potential energy at the top versus at the water level. What happens to the PE as she dives?

Q12. Explain the concept of potential energy using the example of a Jaipur craftsman who pulls back a bowstring to shoot an arrow. Where is the energy stored and what form does it take when the arrow flies?

Q13. Derive the expression for gravitational potential energy (PE = mgh). Your derivation must include:
(a) defining the work needed to lift an object of mass m through height h against gravity,
(b) the force required equals mg (upward),
(c) substituting into W = F × h to get W = mgh,
(d) explaining that this work is stored as PE,
(e) giving the unit and one example from Indian daily life.

Q14. A 75 kg man climbs a staircase at Charminar, Hyderabad, from ground level to a height of 18 m.
(a) Calculate the gravitational PE gained.
(b) If he then climbs a further 6 m to a higher floor, what is his total PE from ground?
(c) Calculate the increase in PE between the two floors.
(d) If he then walks horizontally at the same height for 20 m, does his PE change? Explain.
(e) If he comes back to ground level, what is his final PE and what happened to the energy?

Q15. Analyse the potential energy in the following systems and answer fully:
(a) A 500 g apple hangs from a branch 3 m above the ground — calculate its PE.
(b) A 2 kg stone rests on a 15 m cliff above a valley — calculate its PE.
(c) An archer pulls a bowstring back 0.3 m with a force of 200 N (elastic PE = ½ × F × x) — calculate the stored PE.
(d) Which system has the most PE?
(e) In each case, what form does the PE convert to when released?

Q16. The Bhakra Nangal Dam has water at a height of 200 m. A turbine uses 5000 kg of water per second. (g = 10 m/s²)
(a) Calculate the PE of 5000 kg of water at the top.
(b) If all the PE converts to electrical energy with 80% efficiency, how much useful energy is generated per second?
(c) State the unit of energy per second. What is this physical quantity called?

Q17. A ball of mass 0.4 kg is thrown vertically upward with an initial velocity of 20 m/s. (g = 10 m/s²)
(a) Using v² = u² − 2gh, find the maximum height reached when v = 0.
(b) Calculate the PE at the maximum height.
(c) Calculate the initial KE.
(d) Compare KE at launch and PE at maximum height. What do you notice?

Q18. A child of mass 30 kg sits on a swing. She is pulled back so the seat rises 0.8 m above its lowest position. (g = 10 m/s²)
(a) Calculate the PE gained at the highest point.
(b) If all PE converts to KE at the lowest point, calculate the velocity at the bottom of the swing.
(c) At the midpoint of the swing (height 0.4 m), calculate the KE and PE.
(d) What principle did you use in parts (b) and (c)?