Paper 3 Forces Drills

Q1 Equilibrium of a signboard

A light rigid signboard is held horizontally by a hinge at a wall and a cable attached to the outer end. The signboard length is $1.50\mathrm{m}$. The cable makes an angle of $35^{\circ }$ above the signboard. A sign of weight $90.0\mathrm{N}$ hangs from the board $1.10\mathrm{m}$ from the hinge. The weight of the board is negligible.

1. Explain why taking moments about the hinge is useful. [2]
2. Calculate the tension in the cable. [4]
3. Determine the horizontal and vertical components of the force exerted by the hinge on the board. [4]
4. State one modelling assumption in the calculation. [1]

Q2 Object falling through a fluid

A small metal sphere is released from rest in a tall column of oil. Its weight is $0.420\mathrm{N}$ and the upthrust is $0.060\mathrm{N}$. The resistive force increases with speed.

1. Calculate the initial resultant force on the sphere. [2]
2. Explain why the acceleration decreases as the sphere speeds up. [3]
3. Calculate the resistive force when the sphere has reached terminal velocity. [2]
4. Sketch and explain the shape of a speed-time graph from release to terminal velocity. [4]
5. Explain why terminal velocity would be smaller in a more viscous oil. [2]