Potential Energy – Gravitational and Spring - UNSOLVED PRACTICE SET

Q7. Define gravitational potential energy. Derive the expression U = mgh for a body near the Earth's surface.

Q8. Derive the expression for the potential energy stored in a spring. Why is the factor ½ present in the expression?

Q9. A 2 kg mass is lifted to a height of 5 m. Calculate the increase in its gravitational potential energy. (Take g = 9.8 m/s²)

Q10. In your school laboratory, a spring stretches by 2 cm when a 100 g mass is hung from it. Calculate the spring constant and the potential energy stored in the spring.

Q11. Why is gravitational potential energy negative when measured from infinity? What is the significance of this negative sign?

Q12. Two springs A and B have spring constants in the ratio 2:3. If they are stretched by the same force, compare the potential energies stored in them.

Q13. Explain the concept of potential energy. Distinguish between gravitational and elastic (spring) potential energy. Derive expressions for both. Discuss why potential energy is defined only for conservative forces.

Q14. A 5 kg block is attached to a vertical spring (k = 500 N/m) and slowly lowered to its equilibrium position.

(a) Calculate the extension of the spring at equilibrium.

(b) Calculate the decrease in gravitational potential energy of the block.

(c) Calculate the increase in spring potential energy.

(d) Explain why these two energies are not equal.

(e) Where does the "missing" energy go?

Q15. Two springs with spring constants k₁ = 200 N/m and k₂ = 300 N/m are connected:

(a) In series, with a 5 kg mass hanging from the combination

(b) In parallel, with the same mass hanging from the combination

For each case, calculate:

(i) The equivalent spring constant

(ii) The extension of the system

(iii) The potential energy stored

(iv) Compare the results and discuss which arrangement is stiffer

Q16. A 0.5 kg block is placed against a spring (k = 400 N/m) compressed by 10 cm on a frictionless horizontal surface.

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

(b) When released, what is the maximum kinetic energy of the block?

(c) Calculate the maximum speed of the block.

(d) If the block encounters a rough patch (μ = 0.2) of length 0.5 m after leaving the spring, will it cross the patch?

(e) Calculate the total distance travelled on the rough surface before stopping.

Q17. A pendulum bob of mass 200 g is pulled aside until the string makes 60° with the vertical (string length = 1 m).

(a) Calculate the increase in gravitational potential energy.

(b) Calculate the speed of the bob at the lowest point.

(c) If the string is cut at the lowest point, calculate the horizontal distance travelled before hitting the ground (height of lowest point = 2 m above ground).

(d) Calculate the tension in the string at the lowest point.

(e) What would happen if the bob were given a slight push at the highest point?

Q18. In a school project, students design a "bungee jump" model using an elastic cord (k = 50 N/m, unstretched length 2 m) and a 1 kg mass.

(a) Calculate the extension when the mass hangs at rest.

(b) If the mass is dropped from the point where the cord is just unstretched, calculate the maximum extension.

(c) Calculate the maximum speed during the fall.

(d) At what point during the fall is the speed maximum?

(e) Discuss the energy transformations during the entire motion.