6 Nm
8 Nm
10 Nm
14 Nm
3 A uniform disc has mass 6 kg and diameter 8 cm
A uniform rectangular lamina, \(A B C D\), has mass 4 kg , width 8 cm and length 20 cm
The disc is fixed to the lamina to form a composite body as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-03_448_881_587_577}
The sides \(A B , A D\) and \(C D\) are tangents to the disc.
Calculate the distance of the centre of mass of the composite body from \(A D\)
Circle your answer.
4 cm
5.6 cm
6.4 cm
8.8 cm
4 A car of mass 1400 kg drives around a horizontal circular bend of radius 60 metres.
The car has a constant speed of \(12 \mathrm {~ms} ^ { - 1 }\) on the bend.
Calculate the magnitude of the resultant force acting on the car.
[0pt]
[2 marks]
\(5 \quad\) A region bounded by the curve with equation \(y = 4 - x ^ { 2 }\), the \(x\)-axis and the \(y\)-axis is shown below.
\includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-04_641_380_408_831}
The region is rotated through \(360 ^ { \circ }\) around the \(x\)-axis to create a uniform solid.
5
- Show that the distance of the centre of mass of the solid from the circular face is \(\frac { 5 } { 8 }\)
[0pt]
[5 marks]
5 - The solid is suspended in equilibrium from a point on the edge of the circular face.
Find the angle between the circular face and the horizontal, giving your answer to the nearest degree.
6 In this question use \(g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
A sphere of mass 0.8 kg is attached to one end of a string of length 2 metres.
The other end of the string is attached to a fixed point \(O\)
The sphere is released from rest with the string taut and at an angle of \(30 ^ { \circ }\) to the vertical, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-06_464_218_676_909}
6 - Find the speed of the sphere when it is directly below \(O\)
6 - State one assumption that you made about the string.
6 - As the sphere moves, the string makes an angle \(\theta\) with the downward vertical.
By finding an expression for the tension in the string in terms of \(\theta\), show that the tension is a maximum when the sphere is directly below \(O\)
6
- A physics student conducts an experiment and uses a device to measure the tension in the string when the sphere is directly below \(O\)
They find that the tension is 9.5 newtons.
Explain why this result is reasonable, showing any calculations that you make.