M4 June 2009 Q1

EdexcelOld spec6 marksCollisions: 1 Sphere Oblique

Figure 1: particle moving horizontally strikes a plane inclined at 45 degrees and rebounds at 30 degrees to the plane — Figure 1

A fixed smooth plane is inclined to the horizontal at an angle of 45°. A particle \(P\) is moving horizontally and strikes the plane. Immediately before the impact, \(P\) is moving in a vertical plane containing a line of greatest slope of the inclined plane. Immediately after the impact, \(P\) is moving in a direction which makes an angle of 30° with the inclined plane, as shown in Figure 1.

Find the fraction of the kinetic energy of \(P\) which is lost in the impact. (6)

Mark scheme

Scheme	Marks
CLM along plane: \(\ v\cos 30^\circ = u\cos 45^\circ\)	M1 A1
\(v = u\sqrt{\dfrac{2}{3}}\)	A1
Fraction of KE Lost \(= \dfrac{\frac{1}{2}mu^2 - \frac{1}{2}mv^2}{\frac{1}{2}mu^2} = \dfrac{\frac{1}{2}mu^2 - \frac{1}{2}m\frac{2}{3}u^2}{\frac{1}{2}mu^2} = \dfrac{1}{3}\)	M1 M1 A1
	(6 marks)