Equilibrium of a Particle - UNSOLVED PRACTICE SET

Q7. State the conditions for equilibrium of a particle. Distinguish between static equilibrium and dynamic equilibrium.

Q8. State Lami's theorem. Under what conditions can it be applied?

Q9. A 5 kg block is suspended by two strings as shown (describe verbally): String A makes 30° with the vertical on the left, String B makes 45° with the vertical on the right. Calculate the tension in String A. (Take g = 10 m/s²)

Q10. In your school physics lab, a picture is hung on a wall using a string. The string makes an angle of 20° with the horizontal on both sides. If the picture weighs 4 N, calculate the tension in the string.

Q11. A body of weight W rests on a smooth inclined plane of angle θ. Resolve the weight into components parallel and perpendicular to the plane. What is the force required to keep the body in equilibrium?

Q12. Three forces of magnitudes 3 N, 4 N, and 5 N act on a particle. Can the particle be in equilibrium? Justify your answer.

Q13. Explain the conditions for equilibrium of a particle. Discuss Lami's theorem and derive it using the sine rule. Solve the following problem: A street lamp of weight 200 N is supported by two wires making angles of 30° and 45° with the horizontal. Calculate the tension in each wire.

Q14. A block of mass 10 kg is placed on a smooth inclined plane of inclination 30°. It is held in equilibrium by a horizontal force F.

(a) Draw a free body diagram showing all forces.

(b) Resolve the forces parallel and perpendicular to the plane.

(c) Calculate the magnitude of F.

(d) Calculate the normal reaction of the plane on the block.

(e) What would happen if the plane were rough with μ = 0.2?

Q15. Analyse the equilibrium of a particle under the action of three forces F₁, F₂, and F₃. Show that if the particle is in equilibrium:

(a) The vector sum F₁ + F₂ + F₃ = 0

(b) The forces can be represented by the sides of a triangle taken in order

(c) Lami's theorem holds: F₁/sin α = F₂/sin β = F₃/sin γ

Apply this to find the tensions in the cables supporting a traffic light.

Q16. A 20 kg signboard is suspended from a horizontal beam by two cables making angles of 25° and 35° with the horizontal, on opposite sides.

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

(b) Write the equilibrium equations for horizontal and vertical forces.

(c) Calculate the tension in each cable. (Take g = 9.8 m/s²)

(d) If the maximum tension either cable can withstand is 200 N, is this arrangement safe?

Q17. A 5 kg block is placed on a smooth inclined plane of angle 37° (sin 37° = 0.6, cos 37° = 0.8). It is connected by a light string passing over a smooth pulley to a 3 kg block hanging vertically.

(a) Draw free body diagrams for both blocks.

(b) Calculate the acceleration of the system if released.

(c) Calculate the tension in the string.

(d) What mass should replace the 3 kg block so that the 5 kg block remains in equilibrium on the incline?

Q18. In a school project, students build a model suspension bridge. The main cable supports a deck of weight 500 N at its centre. The cable sags such that it makes angles of 10° with the horizontal at the towers.

(a) Calculate the tension in the cable on each side of the deck.

(b) If the sag is reduced (angles increase to 15°), how does the tension change?

(c) Calculate the new tension.

(d) Why do real suspension bridges have significant sag?

(e) Design considerations: What happens if the cable angle becomes too small?