7 Two snooker balls, one white and one red, have equal mass.
The balls are on a horizontal table \(A B C D\)
The white ball is struck so that it moves at a speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) parallel to \(A B\)
The white ball hits a stationary red ball.
After the collision, the white ball moves at a speed of \(0.8 \mathrm {~ms} ^ { - 1 }\) and at an angle of \(30 ^ { \circ }\) to \(A B\)
After the collision, the red ball moves at a speed \(v \mathrm {~ms} ^ { - 1 }\) and at an angle \(\theta\) to \(C D\)
When the collision takes place, the white ball is the same distance from \(A B\) as the distance the red ball is from CD
The diagram below shows the table and the velocities of the balls after the collision.
\includegraphics[max width=\textwidth, alt={}, center]{0afe3ff2-0af5-4aeb-98c5-1346fa803388-08_595_1370_1121_335}
Not to scale
After the collision, the white ball hits \(A B\) and the red ball hits \(C D\)
Model the balls as particles that do not experience any air resistance.
7
- Explain why the two balls hit the sides of the table at the same time.
7 - Show that \(\theta = 17.0 ^ { \circ }\) correct to one decimal place.
7 - \(\quad\) Find \(v\)
7 - Determine which ball travels the greater distance after the collision and before hitting the side of the table.
Fully justify your answer.
7 - State one possible refinement to the model that you have used.
\(8 \quad\) In this question use \(g\) as \(9.8 \mathrm {~ms} ^ { - 2 }\)
A rope is used to pull a crate, of mass 60 kg , along a rough horizontal surface.
The coefficient of friction between the crate and the surface is 0.4
The crate is at rest when the rope starts to pull on it.
The tension in the rope is 240 N and the rope makes an angle of \(30 ^ { \circ }\) to the horizontal.
When the crate has moved 5 metres, the rope becomes detached from the crate.