Physics 9702 · AS & A Level · Centripetal acceleration
Centripetal acceleration — practice question
A large bowl is formed from a section of a hollow sphere. A small spherical ball is placed in the bowl and is given a horizontal speed. The ball then travels in a horizontal circular path with constant radius, as shown in Fig. 2.1. The forces on the ball are its weight $W$ and the normal reaction force $R$ from the bowl on the ball, as shown in Fig. 2.2. The normal reaction force $R$ makes an angle $\theta$ to the horizontal.
(a(i))[2]
By splitting the reaction force $R$ into two perpendicular components, show that the resultant force $F$ acting on the ball is given by $W = F \tan \theta$.
(a(ii))[1]
State the role of force $F$ in the motion of the ball in the bowl.
(b)[3]
The ball travels in a circular path of radius $14\,\text{cm}$. For this radius, the angle $\theta$ is $28^\circ$. Calculate the speed of the ball.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolution gives: $F = R\cos\theta$” …