9709/42/M/J/25q7 – Mark Scheme

A particle P of mass 3kg is projected with a speed of 8ms^-1 up a line of greatest slope of a rough plane inclined at to the horizontal. P is projected from a point A on the plane and comes to instantaneous rest at a point B on the plane. P then slides back down the plane. The coefficient of friction between P and the plane is .

Using an energy method throughout, find the speed of P at the instant it returns to A. [6 marks]

9709/43/M/J/25q6 – Mark Scheme

The diagram shows the vertical cross-section ABC of a rough waterslide. The section AB is a straight line of length 5m inclined at an angle of to the horizontal, where . The point B is 2.5m above the level of C. A man of mass 80kg, modelled by a particle, slides down the waterslide, starting from rest at A. The coefficient of friction between the man and the straight section of the waterslide is 0.1.

(a) Find the speed of the man at B. [5 marks]

It is given that there is no change in the speed of the man when passing through B and that his speed at C is 11ms^-1.

(b) Find the work done against the resistance force as the man moves from B to C. [4 marks]

9709/41/O/N/24q2 – Mark Scheme

A particle of mass 7.5kg, starting from rest at A, slides down an inclined plane AB. The point B is 12.5 metres vertically below the level of A, as shown in the diagram.

(a) Given that the plane is smooth, use an energy method to find the speed of the particle at B. [2 marks]

(b) It is given instead that the plane is rough and the particle reaches B with a speed of 8ms^-1. The plane is 25m long and the constant frictional force has magnitude F N.

Find the value of F. [3 marks]