Solving Problems Using Free Body Diagrams - UNSOLVED PRACTICE SET

Q7. What is a free body diagram? Why is it important in solving mechanics problems?

Q8. Draw free body diagrams for:

(a) A book resting on a table

(b) A block sliding down a rough inclined plane

(c) A pendulum bob at the lowest point of its swing

Q9. Two blocks A and B are placed one on top of the other on a horizontal surface. A horizontal force F is applied to block A. Draw separate free body diagrams for both blocks.

Q10. In your school, a student pulls a sledge on snow with a rope at an angle θ above the horizontal. Draw the free body diagram of the sledge and identify all forces.

Q11. A block of mass m is suspended by two strings making angles θ₁ and θ₂ with the vertical. Draw the free body diagram and write the equilibrium equations.

Q12. Why should internal forces not be included in a free body diagram? Give an example to illustrate.

Q13. Explain the method of solving mechanics problems using free body diagrams. Discuss the steps involved:

(i) Identify the system

(ii) Draw the free body diagram

(iii) Choose coordinate axes

(iv) Resolve forces

(v) Apply Newton's laws

Illustrate with a detailed example of a block on an inclined plane.

Q14. Two blocks of masses m₁ = 4 kg and m₂ = 6 kg are connected by a light string passing over a frictionless pulley. m₁ is on a rough horizontal table (μ = 0.2) and m₂ hangs vertically.

(a) Draw separate free body diagrams for both blocks.

(b) Write the equations of motion for each block.

(c) Calculate the acceleration of the system.

(d) Calculate the tension in the string.

(e) What would happen if the table were frictionless?

Q15. Three blocks A (2 kg), B (3 kg), and C (5 kg) are placed in contact on a frictionless surface. A horizontal force of 20 N is applied to block A.

(a) Draw free body diagrams for all three blocks.

(b) Calculate the acceleration of the system.

(c) Calculate the contact force between A and B.

(d) Calculate the contact force between B and C.

(e) Verify your answers using Newton's third law.

Q16. A 10 kg block is placed on a rough inclined plane (μ = 0.3) of angle 30°. It is connected by a light string over a frictionless pulley to a 5 kg hanging block.

(a) Draw free body diagrams for both blocks.

(b) Determine the direction of motion (if any).

(c) Calculate the acceleration of the system.

(d) Calculate the tension in the string.

(e) What minimum coefficient of friction would prevent motion?

Q17. A 2000 kg elevator has a maximum upward acceleration of 1.5 m/s². The cable has a maximum tension of 30,000 N.

(a) Draw the free body diagram of the elevator.

(b) Calculate the maximum number of 70 kg passengers the elevator can carry while accelerating upward at 1.5 m/s².

(c) Calculate the tension if the elevator moves at constant velocity with this maximum load.

(d) Calculate the acceleration if the cable tension drops to 20,000 N with the maximum load.

(e) What safety mechanism should be in place?

Q18. In a school project, students design a "Physics Rescue Mission" where a 50 kg crate must be lowered from a height using a rope over a pulley. The crate must descend at a constant velocity.

(a) Draw the free body diagram of the crate.

(b) Calculate the tension required for constant velocity descent.

(c) If the rope can withstand 600 N and a student of mass 40 kg holds the other end, what is the maximum safe acceleration of the crate?

(d) Calculate the time to lower the crate 10 m at this maximum safe acceleration (starting from rest).

(e) Design an improved system using two pulleys and explain the physics advantage.