Edexcel GCE Mechanics M2 January 2013 exam answers review
Two uniform rods AB and BC are rigidly joined at B so that ∠ABC = 90°. Rod AB has length 0.5 m and mass 2 kg. Rod BC has length 2 m and mass 3 kg. The centre of mass of the framework of the two rods is at G.
- Find the distance of G from BC. (2)
- Find the angle between AB and the downward vertical at A.(3)
The distance of G from AB is 0.6 m.
The framework is suspended from A and hangs freely in equilibrium.
ANSWER
Explanation
- Find the value of R.(4)(4)
- Find the new rate of working of the lorry’s engine.(5)
The lorry now travels up a straight road which is inclined at an angle to the horizontal, where sin α = ½. The magnitude of the non-gravitational resistance to motion is R newtons. The lorry travels at a constant speed of 20 m s−1.
ANSWER
Explanation
A ladder, of length 5 m and mass 18 kg, has one end A resting on rough horizontal ground and its other end B resting against a smooth vertical wall. The ladder lies in a vertical plane perpendicular to the wall and makes an angle with the horizontal ground, where tan α= 4/3, as shown in Figure 1. The coefficient of friction between the ladder and the ground is μ. A woman of mass 60 kg stands on the ladder at the point C, where AC = 3 m. The ladder is on the point of slipping. The ladder is modelled as a uniform rod and the woman as a particle.
Find the value of µ.
(9)
ANSWER
Explanation
At time t seconds the velocity of a particle P is [(4t – 5)i + 3j] m s–1. When t = 0, theposition vector of P is (2i + 5j) m, relative to a fixed origin O.
- Find the value of t when the velocity of P is parallel to the vector j. (1)
- Find an expression for the position vector of P at time t seconds.(4)
A second particle Q moves with constant velocity (−2i + cj) m s−1. When t = 0, the position vector of Q is (11i + 2j) m. The particles P and Q collide at the point with position vector (di +14j) m.
Find
- the value of c,
- the value of d.
(5)
ANSWER
Explanation
The point A lies on a rough plane inclined at an angle to the horizontal, where sin θ = 24/25. A particle P is projected from A, up a line of greatest slope of the plane, with speed U ms−1. The mass of P is 2 kg and the coefficient of friction between P and the plane is 5/12. The particle comes to instantaneous rest at the point B on the plane, where AB =1 5 . m. It then moves back down the plane to A.
- Find the work done against friction as P moves from A to B. (3)
- he work-energy principle to find the value of U. (4)
- Find the speed of P when it returns to A. (3)
ANSWER
Explanation
A ball is thrown from a point O, which is 6 m above horizontal ground. The ball is projected with speed u m s−1 at an angle θ above the horizontal. There is a thin vertical post which is 4 m high and 8 m horizontally away from the vertical through O, as shown in Figure 2. The ball passes just above the top of the post 2 s after projection. The ball is modelled as a particle.
- Show that tan θ = 2.2(5)
- Find the value of u. (2)
- Find the value of T. (3)
- Find α (5).
The ball hits the ground T seconds after projection.
Immediately before the ball hits the ground the direction of motion of the ball makes an angle α with the horizontal.
ANSWER
Explanation
A particle A of mass m is moving with speed u on a smooth horizontal floor when it collides directly with another particle B, of mass 3m, which is at rest on the floor. The coefficient of restitution between the particles is e. The direction of motion of A is reversed by the collision.
- Find, in terms of e and u,
- the speed of A immediately after the collision,
- the speed of B immediately after the collision.
(7)
- find the range of possible values of e,(6)
- determine whether there will be a second collision between A and B.(3)
After being struck by A the particle B collides directly with another particle C, of mass 4m, which is at rest on the floor. The coefficient of restitution between B and C is 2e. Given that the direction of motion of B is reversed by this collision,
ANSWER
Explanation
