Work Done by Constant and Variable Force - UNSOLVED PRACTICE SET

Q7. Define work done by a constant force. When is the work done by a force positive, negative, and zero? Give one example of each.

Q8. A coolie carries a load of 50 kg on his head and walks 100 m on a level road. Calculate the work done by the coolie against gravity.

Q9. Explain how work done by a variable force is calculated using integration. Why can't we simply use W = Fd for variable forces?

Q10. In your school, a student pushes a 10 kg box across the floor with a horizontal force of 40 N through a distance of 5 m. Calculate the work done by the applied force and the work done by friction if μₖ = 0.3.

Q11. A spring follows Hooke's law F = −kx. Derive the expression for work done in stretching the spring from its natural length to an extension x.

Q12. A force F varies with displacement x as F = 3x² + 2x (in SI units). Calculate the work done by this force as the body moves from x = 0 to x = 2 m.

Q13. Explain the concept of work done by a constant force and a variable force. For a variable force, show that the work done is equal to the area under the force-displacement graph. Discuss the significance of the sign of work done in physics.

Q14. A body of mass 2 kg is acted upon by a force that varies with position as shown (describe verbally): From x = 0 to x = 4 m, F increases linearly from 0 to 8 N. From x = 4 m to x = 8 m, F remains constant at 8 N. From x = 8 m to x = 12 m, F decreases linearly to 0.

(a) Calculate the work done in each segment.

(b) Calculate the total work done from x = 0 to x = 12 m.

(c) If the body starts from rest, what is its kinetic energy at x = 12 m?

(d) Sketch the force-displacement graph.

Q15. Analyse the following situations and calculate the work done in each case:

(i) A 60 kg person climbs a staircase of height 4 m

(ii) The same person holds a 20 kg suitcase at chest height for 5 minutes

(iii) The person lowers the suitcase slowly by 1 m

(iv) The person drops the suitcase from 1 m height

Discuss why the work done differs in each case despite involving the same force (gravity).

Q16. A 5 kg block is pulled along a rough horizontal surface (μ = 0.2) by a force of 30 N applied at an angle of 30° above the horizontal. The block moves 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 block.

(d) Calculate the work done by the normal reaction and gravity.

(e) If the block starts from rest, what is its speed after moving 10 m?

Q17. A particle moves along the x-axis under the influence of a force F(x) = 6x − 2x² (F in newtons, x in metres).

(a) Calculate the work done by this force as the particle moves from x = 0 to x = 3 m.

(b) Find the position where the force is zero.

(c) At what position is the force maximum in the range 0 ≤ x ≤ 3 m?

(d) Sketch the force-displacement graph from x = 0 to x = 3 m.

(e) A student claims the work done from x = 0 to x = 3 m equals the work from x = 3 m to x = 0. Is this correct? Explain.

Q18. In a school experiment, students measure the force required to stretch a spring. They record the following data:

Table

Extension x (cm) 0 1 2 3 4 5

Force F (N) 0 2 4 6 8 10

(a) Verify if the spring obeys Hooke's law.

(b) Calculate the spring constant.

(c) Calculate the work done in stretching the spring from x = 0 to x = 5 cm using graphical method.

(d) Calculate the same work using the formula W = ½kx² and compare.

(e) What would be the work done in stretching from x = 3 cm to x = 5 cm?