# WME01 Mechanics 1 (M1) January 2022 Paper 01

Pearson Edexcel International A Level WME01 Mechanics 1 (M1) past paper 01, January 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wme01/2022-january-paper-01/
- PDF: https://mathvsarham.com/papers/wme01/WME01_january_2022_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WME01 Mechanics 1 (M1) (https://mathvsarham.com/past-papers/wme01/)
- Session: January 2022
- Paper: 01
- Component code: WME01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 28

## Question paper text

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

Question 1
[Diagram or table: see page 2 of the paper]
A particle P of weight 5 N is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point O. The particle P is held in equilibrium by a force of magnitude F newtons. The direction of this force is perpendicular to the string and OP makes an angle of 60° with the vertical, as shown in Figure 1.
Find
(a) the value of F [3]
(b) the tension in the string. [3]

Question 2
A particle P has mass km and a particle Q has mass m. The particles are moving towards each other in opposite directions along the same straight line when they collide directly.
Immediately before the collision, P has speed 3u and Q has speed u.
As a result of the collision, the direction of motion of each particle is reversed and the speed of each particle is halved.
(a) Find the value of k. [4]
(b) Find, in terms of m and u, the magnitude of the impulse exerted on Q in the collision. [3]

Question 3
[Diagram or table: see page 6 of the paper]
A beam ADCB has length 5 m. The beam lies on a horizontal step with the end A on the step and the end B projecting over the edge of the step. The edge of the step is at the point D where DB = 1.3 m, as shown in Figure 2.
When a small boy of mass 30 kg stands on the beam at C, where CB = 0.5 m, the beam is on the point of tilting.
The boy is modelled as a particle and the beam is modelled as a uniform rod.
(a) Find the mass of the beam. [3]
A block of mass X kg is now placed on the beam at A.
The block is modelled as a particle.
(b) Find the smallest value of X that will enable the boy to stand on the beam at B without the beam tilting. [3]
(c) State how you have used the modelling assumption that the block is a particle in your calculations. [1]

Question 4
At time t = 0, a small ball is projected vertically upwards from a point A which is 24.5 m above the ground. The ball first comes to instantaneous rest at the point B, where AB = 19.6 m and first hits the ground at time t = T seconds.
The ball is modelled as a particle moving freely under gravity.
(a) Find the value of T. [6]
(b) Sketch a speed-time graph for the motion of the ball from t = 0 to t = T seconds.
(No further calculations are needed in order to draw this sketch.) [2]

Question 5
[Diagram or table: see page 14 of the paper]
A particle of mass m rests in equilibrium on a fixed rough plane under the action of a force of magnitude X. The force acts up a line of greatest slope of the plane, as shown in Figure 3.
The plane is inclined at an angle α to the horizontal, where tan α = 3/4
The coefficient of friction between the particle and the plane is μ.
• When X = 2P, the particle is on the point of sliding up the plane.
• When X = P, the particle is on the point of sliding down the plane.
Find the value of μ. [8]

Question 6
[In this question i and j are horizontal unit vectors.]
A particle P of mass 2 kg moves under the action of two forces, ( pi + qj) N and (2qi + pj) N , where p and q are constants.
Given that the acceleration of P is (i − j) m s^−2
(a) find the value of p and the value of q. [5]
(b) Find the size of the angle between the direction of the acceleration and the vector j. [2]
At time t = 0, the velocity of P is (3i − 4j) m s^−1
At t = T seconds, P is moving in the direction of the vector (11i − 13j).
(c) Find the value of T. [5]

Question 7
[Diagram or table: see page 22 of the paper]
A particle P of mass 4m lies on the surface of a fixed rough inclined plane.
The plane is inclined to the horizontal at an angle α where tan α = 3/4
The particle P is attached to one end of a light inextensible string.
The string passes over a small smooth pulley that is fixed at the top of the plane. The other end of the string is attached to a particle Q of mass m which lies on a smooth horizontal plane.
The string lies along the horizontal plane and in the vertical plane that contains the pulley and a line of greatest slope of the inclined plane.
The system is released from rest with the string taut, as shown in Figure 4, and P moves down the plane.
The coefficient of friction between P and the plane is 1/4
For the motion before Q reaches the pulley
(a) write down an equation of motion for Q, [1]
(b) find, in terms of m and g, the tension in the string, [7]
(c) find the magnitude of the force exerted on the pulley by the string. [4]
(d) State where in your working you have used the information that the string is light. [1]

Question 8
[In this question i and j are horizontal unit vectors directed due east and due north respectively and position vectors are given relative to a fixed origin.]
A ship A moves with constant velocity (3i – 10j) km h^−1
At time t hours, the position vector of A is r km.
At time t = 0, A is at the point with position vector (13i + 5j) km.
(a) Find r in terms of t. [2]
Another ship B moves with constant velocity (15i + 14j) km h^−1
At time t = 0, B is at the point with position vector (3i – 5j) km.
(b) Show that, at time t hours,
[Diagram or table: see page 26 of the paper]
[4]
Given that the two ships do not change course,
(c) find the shortest distance between the two ships, [6]
(d) find the bearing of ship B from ship A when the ships are closest. [2]
[Diagram or table: see page 28 of the paper]