# WME01 Mechanics 1 (M1) Oct/Nov 2021 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wme01/2021-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wme01/WME01_oct-nov_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: Oct/Nov 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
[Diagram or table: see page 2 of the paper]
A non‑uniform rod AB has length 9 m and mass M kg.
The rod rests in equilibrium in a horizontal position on two supports, one at C where AC = 2.5 m and the other at D where DB = 2 m, as shown in Figure 1.
The magnitude of the force acting on the rod at D is twice the magnitude of the force acting on the rod at C.
The centre of mass of the rod is d metres from A.
Find the value of d. [6]

Question 2
A particle P of mass 2m is moving on a rough horizontal plane when it collides directly with a particle Q of mass 4m which is at rest on the plane. The speed of P immediately before the collision is 3u. The speed of Q immediately after the collision is 2u.
(a) Find, in terms of u, the speed of P immediately after the collision. [3]
(b) State clearly the direction of motion of P immediately after the collision. [1]
Following the collision, Q comes to rest after travelling a distance 6u/g along the plane.
The coefficient of friction between Q and the plane is μ.
(c) Find the value of μ. [6]

Question 3
A car is moving at a constant speed of 25 m s^–1 along a straight horizontal road.
The car is modelled as a particle.
At time t = 0, the car is at the point A and the driver sees a road sign 48 m ahead.
Let t seconds be the time that elapses after the car passes A.
In a first model, the car is assumed to decelerate uniformly at 6 m s^–2 from A until the car reaches the road sign.
(a) Use this first model to find the speed of the car as it reaches the sign. [2]
The road sign indicates that the speed limit immediately after the sign is 13 m s^–1.
In a second model, the car is assumed to decelerate uniformly at 6 m s^–2 from A until it reaches a speed of 13 m s^–1. The car then maintains this speed until it reaches the road sign.
(b) Use this second model to find the value of t at which the car reaches the sign. [4]
In a third model, the car is assumed to move with constant speed 25 m s^–1 from A until time t = 0.2, the car then decelerates uniformly at 6 m s^–2 until it reaches a speed of 13 m s^–1. The car then maintains this speed until it reaches the road sign.
(c) Use this third model to find the value of t at which the car reaches the sign. [4]

Question 4
The position vector, r metres, of a particle P at time t seconds, relative to a fixed origin O, is given by
[Diagram or table: see page 14 of the paper]
(a) Find, to the nearest degree, the size of the angle between r and the vector j, when t = 2 [3]
(b) Find the values of t for which the distance of P from O is 2.5 m. [5]

Question 5
[Diagram or table: see page 18 of the paper]
A small bead of mass 0.2 kg is attached to the end P of a light rod PQ. The bead is threaded onto a fixed vertical rough wire.
The bead is held in equilibrium with the rod PQ inclined to the wire at an angle α, where
tan α = 4/3 , as shown in Figure 2.
The thrust in the rod is T newtons.
The bead is modelled as a particle.
(a) Find the magnitude and direction of the friction force acting on the bead when T = 2.5 [3]
The coefficient of friction between the bead and the wire is μ.
Given that the greatest possible value of T is 6.125
(b) find the value of μ. [7]

Question 6
[Diagram or table: see page 22 of the paper]
A small ball is thrown vertically upwards at time t = 0 from a point A which is above horizontal ground. The ball hits the ground 7 s later.
The ball is modelled as a particle moving freely under gravity.
The velocity‑time graph shown in Figure 3 represents the motion of the ball for 0  t  7
(a) Find the speed with which the ball is thrown. [2]
(b) Find the height of A above the ground. [3]

Question 7
[Diagram or table: see page 24 of the paper]
One end of a light inextensible string is attached to a particle A of mass 2m. The other end of the string is attached to a particle B of mass 3m. The string passes over a small, smooth, light pulley P which is fixed at the top of a rough inclined plane. The plane is inclined to
the horizontal at an angle α, where tan α = 3/4
Particle A is held at rest on the plane with the string taut and B hanging freely below P, as shown in Figure 4. The section of the string AP is parallel to a line of greatest slope of the plane.
The coefficient of friction between A and the plane is 1/2
Particle A is released and begins to move up the plane.
For the motion before A reaches the pulley,
(a)(i) write down an equation of motion for A,
(ii) write down an equation of motion for B, [4]
(b) find, in terms of g, the acceleration of A, [5]
(c) find the magnitude of the force exerted on the pulley by the string. [4]
(d) State how you have used the information that P is a smooth pulley. [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.]
At 7 am a ship leaves a port and moves with constant velocity. The position vector of the port is (–2i + 9j) km.
At 7.36 am the ship is at the point with position vector (4i + 6j) km.
(a) Show that the velocity of the ship is (10i – 5j) km h^–1 [2]
(b) Find the position vector of the ship t hours after leaving port. [2]
At 8.48 am a passenger on the ship notices that a lighthouse is due east of the ship.
At 9 am the same passenger notices that the lighthouse is now north east of the ship.
(c) Find the position vector of the lighthouse. [4]
(d) Find the position vector of the ship when it is due south of the lighthouse. [4]
[Diagram or table: see page 32 of the paper]