# WME01 Mechanics 1 (M1) May/June 2021 Paper 01

Pearson Edexcel International A Level WME01 Mechanics 1 (M1) past paper 01, May/June 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wme01/2021-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wme01/WME01_may-june_2021_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WME01 Mechanics 1 (M1) (https://mathvsarham.com/past-papers/wme01/)
- Session: May/June 2021
- Paper: 01
- Component code: WME01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 32

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
A particle P has mass 3m and a particle Q has mass 5m. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly.
Immediately before the collision the speed of P is ku, where k is a constant, and the speed of Q is 2u.
Immediately after the collision the speed of P is u and the speed of Q is 3u.
The direction of motion of Q is reversed by the collision.
(a) Find, in terms of m and u, the magnitude of the impulse exerted on Q by P in the collision. [2]
(b) Find the two possible values of k. [5]
[Diagram or table: see page 2 of the paper]
[Diagram or table: see page 3 of the paper]

Question 2
A car moves along a straight horizontal road with constant acceleration a m s^–2 where a > 0
The car is modelled as a particle.
At time t = 0, the car passes point A and is moving with speed u m s^–1
In the first three seconds after passing A the car travels 20 m.
In the fourth second after passing A the car travels 10 m.
The speed of the car as it passes point B is 20 m s^–1
Find the time taken for the car to travel from A to B. [8]
[Diagram or table: see page 4 of the paper]
[Diagram or table: see page 5 of the paper]
[Diagram or table: see page 6 of the paper]
[Diagram or table: see page 7 of the paper]

Question 3
[In this question i and j are perpendicular horizontal unit vectors.]
Three forces, F_1, F_2 and F_3, are given by
[Diagram or table: see page 8 of the paper]
where a and b are constants.
The forces F_1, F_2 and F_3 act on a particle P of mass 4 kg.
Given that P rests in equilibrium on a smooth horizontal surface under the action of these three forces,
(a) find the size of the angle between the direction of F_3 and the direction of – j. [4]
The force F_3 is now removed and replaced by the force F_4 given by F_4= λ (i + 3j) N, where λ is a positive constant.
When the three forces F_1, F_2 and F_4 act on P, the acceleration of P has magnitude 3.25 m s^–2
(b) Find the value of λ. [5]
[Diagram or table: see page 8 of the paper]
[Diagram or table: see page 9 of the paper]
[Diagram or table: see page 10 of the paper]
[Diagram or table: see page 11 of the paper]

Question 4
[Diagram or table: see page 12 of the paper]
Figure 1 shows a large bucket used by a crane on a building site to move materials between the ground and the top of the building. The mass of the bucket is 15 kg.
The bucket is attached to a vertical cable with the bottom of the bucket horizontal. The cable is modelled as light and inextensible.
When the bucket is on the ground, a bag of cement of mass 25 kg is placed in the bucket.
The bucket with the bag of cement moves vertically upwards with constant acceleration 0.2 m s^–2. Air resistance is modelled as being negligible.
(a) Find the tension in the cable. [3]
At the top of the building, the bag of cement is removed. A box of tools of mass 12 kg is now placed in the bucket.
Later on the bucket with the box of tools is moving vertically downwards with constant deceleration 0.1 m s^–2. Air resistance is again modelled as being negligible.
(b) Find the magnitude of the normal reaction between the bucket and the box of tools. [3]
[Diagram or table: see page 12 of the paper]
[Diagram or table: see page 13 of the paper]
[Diagram or table: see page 14 of the paper]
[Diagram or table: see page 15 of the paper]

Question 5
[In this question i and j are perpendicular horizontal unit vectors.]
A particle P is moving with constant acceleration. At 2 pm, the velocity of P is (3i + 5j) km h^–1 and at 2.30 pm the velocity of P is (i + 7j) km h^–1
At time T hours after 2 pm, P is moving in the direction of the vector (– i + 2j)
(a) Find the value of T. [6]
Another particle, Q, has velocity v_Q km h^–1 at time t hours after 2 pm, where
[Diagram or table: see page 16 of the paper]
and μ is a constant.
Given that there is an instant when the velocity of P is equal to the velocity of Q,
(b) find the value of μ. [3]
[Diagram or table: see page 16 of the paper]
[Diagram or table: see page 17 of the paper]
[Diagram or table: see page 18 of the paper]
[Diagram or table: see page 19 of the paper]

Question 6
A fixed rough plane is inclined at an angle θ to the horizontal, where tan θ = 5/12
A particle of mass 6 kg is projected with speed 5 m s^–1 from a point A on the plane, up a line of greatest slope of the plane.
The coefficient of friction between the particle and the plane is 1/4
(a) Find the magnitude of the frictional force acting on the particle as it moves up the plane. [3]
The particle comes to instantaneous rest at the point B.
(b) Find the distance AB. [5]
The particle now slides down the plane from B. At the instant when the particle passes through the point C on the plane, the speed of the particle is again 5 m s^–1
(c) Find the distance BC. [5]
[Diagram or table: see page 20 of the paper]
[Diagram or table: see page 21 of the paper]
[Diagram or table: see page 22 of the paper]
[Diagram or table: see page 23 of the paper]

Question 7
[Diagram or table: see page 24 of the paper]
A non-uniform beam AB, of mass 60 kg and length 8a metres, rests in equilibrium in a horizontal position on two vertical supports. One support is at C, where AC = a metres and the other support is at D, where DB = 2a metres, as shown in Figure 2.
The magnitude of the normal reaction between the beam and the support at D is three times the magnitude of the normal reaction between the beam and the support at C.
By modelling the beam as a non-uniform rod whose centre of mass is at a distance x metres from A,
(a) find an expression for x in terms of a. [5]
A box of mass M kg is placed on the beam at E, where AE = 2a metres.
The beam remains in equilibrium in a horizontal position.
The magnitude of the normal reaction between the beam and the support at C is now equal to the magnitude of the normal reaction between the beam and the support at D.
By modelling the box as a particle,
(b) find the value of M. [5]
[Diagram or table: see page 24 of the paper]
[Diagram or table: see page 25 of the paper]
[Diagram or table: see page 26 of the paper]
[Diagram or table: see page 27 of the paper]

Question 8
Two trams, tram A and tram B, run on parallel straight horizontal tracks. Initially the two trams are at rest in the depot and level with each other.
At time t = 0, tram A starts to move. Tram A moves with constant acceleration 2 m s ^–2 for 5 seconds and then continues to move along the track at constant speed.
At time t = 20 seconds, tram B starts from rest and moves in the same direction as tram A. Tram B moves with constant acceleration 3 m s ^–2 for 4 seconds and then continues to move along the track at constant speed.
The trams are modelled as particles.
(a) Sketch, on the same axes, a speed-time graph for the motion of tram A and a speed-time graph for the motion of tram B, from t = 0 to the instant when tram B overtakes tram A. [3]
At the instant when the two trams are moving with the same speed, tram A is d metres in front of tram B.
(b) Find the value of d. [5]
(c) Find the distance of the trams from the depot at the instant when tram B overtakes tram A. [5]
[Diagram or table: see page 28 of the paper]
[Diagram or table: see page 29 of the paper]
[Diagram or table: see page 30 of the paper]
[Diagram or table: see page 31 of the paper]
[Diagram or table: see page 32 of the paper]
[Diagram or table: see page 32 of the paper]