Practice Paper 3 (Mechanics) (Edexcel A Level Maths: Pure)

Two particles A and B, of masses 2.7 kg and 2.2 kg respectively, are connected by means of a light inextensible string.  Particle A is held motionless on a rough fixed plane inclined at 25° to the horizontal.  The string passes over a smooth light pulley fixed at the top of the plane so that B is hanging vertically downwards as shown in the diagram below:

The string between A and the pulley lies along a line of greatest slope of the plane, and B hangs freely from the pulley.  The coefficient of friction between particle A and the plane is μ.

The system is released from rest with the string taut.  Given that particle B descends 1.82 m in the first 3 seconds after it is released, find the value of μ.

In the following diagram AB is a ladder of length 2a and mass m_l.  End A of the ladder is resting against a rough vertical wall, while end B rests on rough horizontal ground so that the ladder makes an angle of θ with the ground as shown below:

A person with mass m_p is standing on the ladder a distance d from end B. The ladder may be modelled as a uniform rod lying in a vertical plane which is perpendicular to the wall, and the person may be modelled as a particle. The coefficient of friction between the wall and the ladder is μ_A, and the coefficient of friction between the ground and the ladder is μ_B. It may be assumed that .

Given that the ladder is at rest in limiting equilibrium, show that

where R_B is the normal reaction force exerted by the ground on the ladder at point B and where g is the constant of acceleration due to gravity.

In this question, use  for the acceleration due to gravity.

The graph below shows the trajectory of a projectile, with x and y being measured in metres.

Use the graph to help determine

the initial velocity of the projectile in the form

At time t seconds, a particle P has acceleration a m s⁻², where

                               .

Initially P starts at the origin O and moves with velocity .

Find the distance between the origin and the position P of when .

Find the value of t at the instant when P is moving in the direction of .

A snooker ball is struck such that it travels in a straight line up and down a snooker table. The graph below shows the velocity of the ball, , at time  after being struck.

When the snooker ball comes to rest it has displacement 0.3 m. Find the value of T and the total distance travelled by the ball.

Two particles A and B have masses of 3 kg and m_B kg respectively. The particles are connected by a light inextensible string that passes over a smooth light fixed pulley as shown in the diagram below:

The particles are released from rest with the string taut and particle A begins to accelerate downwards at a rate of .

Find the value of m_B.