Momentum, impulse and collisions requiring resolvingAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

Which impulse acts when smooth spheres collide?
What happens to the component of velocity perpendicular to the impulse?
Oblique impact with a smooth wall: parallel component after?
Perpendicular component after an impact with a wall?
Speed after an oblique impact (angle \theta to wall)?
Relationship between angles before and after (to the wall)?
Impulse on a particle from a wall (angle \theta to the wall)?
Two smooth spheres: what do you apply along the line of centres?
How do you find the final speed of a sphere?
If \tan\alpha=\frac43, find \sin\alpha and \cos\alpha.
For an angle \theta measured to the wall, which gives the parallel component?
Kinetic energy lost in an oblique collision depends on which components?
Why is the perpendicular component unchanged for smooth spheres?

Exam questions on Momentum, impulse and collisions requiring resolving

A smooth ball of mass $0.2$ kg hits a fixed smooth vertical wall with speed $10$ m s⁻¹. Its direction of motion before the impact makes an angle of $60^\circ$ with the wall. The coefficient of restitution between the ball and the wall is $0.5$ .
Find the speed of the ball immediately after the impact.2 marks
A smooth ball of mass $0.3$ kg moves on a smooth horizontal floor with velocity $(8\mathbf{i}-6\mathbf{j})$ m s⁻¹ and hits a fixed smooth vertical wall that is parallel to the vector $\mathbf{i}$ . The coefficient of restitution between the ball and the wall is $0.75$ . Here $\mathbf{i}$ and $\mathbf{j}$ are perpendicular horizontal unit vectors.
Find the angle through which the direction of motion of the ball is deflected by the impact.2 marks
A smooth sphere of mass $0.5$ kg hits a fixed smooth vertical wall with speed $20$ m s⁻¹. Before the impact its direction of motion makes an angle $\alpha$ with the wall, where $\tan\alpha=\frac43$ . The coefficient of restitution between the sphere and the wall is $\frac34$ .
Find the speed of the sphere immediately after the impact.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).