Edexcel A Level Further Maths Paper 3C: Further Mechanics 1 October 2020 question paper 9FM0/3C

A particle P of mass 0.5 kg is moving with velocity (4i + 3j) m s^–1 when it receives an impulse J N s. Immediately after receiving the impulse, P is moving with velocity (–i + 6j) m s^–1.

Find the magnitude of J.

The angle between the direction of the impulse and the direction of motion of P immediately before receiving the impulse is α

Find the value of α

A truck of mass 1200 kg is moving along a straight horizontal road.

At the instant when the speed of the truck is vm s^–1, the resistance to the motion of the truck is modelled as a force of magnitude (900 + 9 v) N.

The engine of the truck is working at a constant rate of 25 kW.

Find the deceleration of the truck at the instant when v = 25

Later on, the truck is moving up a straight road that is inclined at an angle θ to the

At the instant when the speed of the truck is vm s^–1, the resistance to the motion of the truck from non‑gravitational forces is modelled as a force of magnitude (900 + 9 v) N.

When the engine of the truck is working at a constant rate of 25 kW the truck is moving up the road at a constant speed of Vm s^–1.

Find the value of V.

Two particles, A and B, have masses 3m and 4m respectively. The particles are moving in the same direction along the same straight line on a smooth horizontal surface when they collide directly. Immediately before the collision the speed of A is 2 u and the speed of B is u.

The coefficient of restitution between A and B is e.

Show that the direction of motion of each of the particles is unchanged by the collision.

After the collision with A, particle B collides directly with a third particle, C, of mass 2m, which is at rest on the surface.

The coefficient of restitution between B and C is also e.

Show that there will be a second collision between A and B.

[In this question, i and j are perpendicular unit vectors in a horizontal plane.]

Figure 1 represents the plan view of part of a smooth horizontal floor, where AB represents a fixed smooth vertical wall.

A small ball of mass 0.5 kg is moving on the floor when it strikes the wall.

Immediately before the impact the velocity of the ball is (7i + 2j) m s^–1.

Immediately after the impact the velocity of the ball is (i + 6j) m s^–1.

The coefficient of restitution between the ball and the wall is e.

Show that AB is parallel to (2i + 3j).

Find the value of e.

A smooth uniform sphere P has mass 0.3 kg. Another smooth uniform sphere Q, with the same radius as P, has mass 0.2 kg.

The spheres are moving on a smooth horizontal surface when they collide obliquely. Immediately before the collision the velocity of P is (4i + 2j) m s^–1 and the velocity of Q is (–3i + j) m s^–1.

At the instant of collision, the line joining the centres of the spheres is parallel to i.

The kinetic energy of Q immediately after the collision is half the kinetic energy of Q immediately before the collision.

Find

the velocity of P immediately after the collision,

the velocity of Q immediately after the collision,

the coefficient of restitution between P and Q,

carefully justifying your answers.

Find the size of the angle through which the direction of motion of P is deflected by the collision.

A light elastic string with natural length l and modulus of elasticity kmg has one end attached to a fixed point A on a rough inclined plane. The other end of the string is attached to a package of mass m. The plane is inclined at an angle θ to the horizontal, where tanθ =

The coefficient of friction between the package and the plane is

By modelling the package as a particle,

find the acceleration of the package at the instant it starts to move back down the plane from the point B.

Figure 2 represents the plan view of part of a horizontal floor, where AB and CD represent fixed vertical walls, with AB parallel to CD.

A small ball is projected along the floor towards wall AB. Immediately before hitting wall AB, the ball is moving with speed vm s^–1 at an angle α to AB, where 0 < α < The ball hits wall AB and then hits wall CD. After the impact with wall CD, the ball is moving at angle α to CD. The coefficient of restitution between the ball and wall AB is The coefficient of restitution between the ball and wall CD is also The floor and the walls are modelled as being smooth. The ball is modelled as a particle.

Find the percentage of the initial kinetic energy of the ball that is lost as a result of the two impacts.