OCR MEI
Further Mechanics Major
2020
November
— Question 9
Exam Board
OCR MEI
Module
Further Mechanics Major (Further Mechanics Major)
Year
2020
Session
November
Topic
Circular Motion 1
Determine, in terms of \(W\) and \(\theta\), the tension in the string.
It is given that, for equilibrium to be possible, the greatest distance the ring can be from A is \(2.4 a\).
Determine the coefficient of friction between the bar and the ring.
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Fig. 10 shows a small bead P of mass \(m\) which is threaded on a smooth thin wire. The wire is in the form of a circle of radius \(a\) and centre O . The wire is fixed in a vertical plane.
The bead is initially at the lowest point A of the wire and is projected along the wire with a velocity which is just sufficient to carry it to the highest point on the wire. The angle between OP and the downward vertical is denoted by \(\theta\).
Determine the value of \(\theta\) when the magnitude of the reaction of the wire on the bead is \(\frac { 7 } { 2 } m g\).
Show that the angular velocity of P when OP makes an angle \(\theta\) with the downward vertical is given by \(k \sqrt { \frac { g } { a } } \cos \left( \frac { \theta } { 2 } \right)\), stating the value of the constant \(k\).
Hence determine, in terms of \(g\) and \(a\), the angular acceleration of P when \(\theta\) takes the value found in part (a).