20 J
4 Reena is skating on an ice rink, which has a horizontal surface.
She follows a circular path of radius 5 metres and centre \(O\)
She completes 10 full revolutions in 1 minute, moving with a constant angular speed of \(\omega\) radians per second.
The mass of Reena is 40 kg
4
- Find the value of \(\omega\)
4 - Find the magnitude of the horizontal resultant force acting on Reena.
4
- (ii) Show the direction of this horizontal resultant force on the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-03_380_442_2017_861}
5 An impulse of \(\left[ \begin{array} { r } - 5
12 \end{array} \right] \mathrm { N } \mathrm { s }\) is applied to a particle of mass 5 kg which is moving with velocity \(\left[ \begin{array} { l } 6
2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }\)
5 - Calculate the magnitude of the impulse.
5
- Find the speed of the particle immediately after the impulse is applied.
6 A ball is thrown with speed \(u\) at an angle of \(45 ^ { \circ }\) to the horizontal from a point \(O\)
When the horizontal displacement of the ball is \(x\), the vertical displacement of the ball above \(O\) is \(y\) where
$$y = x - \frac { k x ^ { 2 } } { u ^ { 2 } }$$
6 - Use dimensional analysis to find the dimensions of \(k\)
6 - State what can be deduced about \(k\) from the dimensions that you found in part (a).
7 Two smooth, equally sized spheres, \(A\) and \(B\), are moving in the same direction along a straight line on a smooth horizontal surface, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-06_314_465_420_849}
The spheres subsequently collide.
Immediately after the collision, \(A\) has speed \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) has speed \(3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
The coefficient of restitution between the spheres is \(e\)
7 - Show that \(A\) does not change its direction of motion as a result of the collision.
7
- (ii) Find the value of \(e\)
7 - Given that the mass of \(B\) is 0.6 kg , find the mass of \(A\)