# WME01 Mechanics 1 (M1) May/June 2023 Paper 01

Pearson Edexcel International A Level WME01 Mechanics 1 (M1) past paper 01, May/June 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wme01/2023-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wme01/WME01_may-june_2023_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 2023
- 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
A particle A has mass 4 kg and a particle B has mass 2 kg.
The particles move towards each other in opposite directions along the same straight line on a smooth horizontal table and collide directly.
Immediately before the collision, the speed of A is 2u m s^–1 and the speed of B is 3u m s^–1
Immediately after the collision, the speed of B is 2u m s^–1
The direction of motion of B is reversed by the collision.
(a) Find, in terms of u, the speed of A immediately after the collision. [3]
(b) State the direction of motion of A immediately after the collision. [1]
(c) Find, in terms of u, the magnitude of the impulse received by B in the collision. State the units of your answer. [3]
[Diagram or table: see page 4 of the paper]

Question 2
A particle P rests in equilibrium on a smooth horizontal plane.
A system of three forces, F_1 N, F_2 N and F_3 N where
[Diagram or table: see page 4 of the paper]
is applied to P.
Given that P remains in equilibrium,
(a) find F_3 in terms of c, i and j. [2]
The force F_3 is removed from the system.
Given that c = 2
(b) find the size of the angle between the direction of i and the direction of the resultant force acting on P. [4]
The mass of P is m kg.
Given that the magnitude of the acceleration of P is 8.5 m s^–2
(c) find the value of m. [4]

Question 3
Two students observe a book of mass 0.2 kg fall vertically from rest from a shelf that is 1.5 m above the floor.
Student A suggests that the book is modelled as a particle falling freely under gravity.
(a) Use student A’s model to find the time taken for the book to reach the floor. [3]
Student B suggests an improved model where the book is modelled as a particle experiencing a constant resistance to motion of magnitude R newtons.
Given that the time taken for the book to reach the floor is 0.6 seconds,
(b) use student B’s model to find the value of R [5]

Question 4
[Diagram or table: see page 8 of the paper]
Figure 1 shows a beam AB, of mass m kg and length 2 m, suspended by two light vertical ropes. The ropes are attached to the points C and D on the beam, where AC = 0.6 m and DB = 0.2 m The beam is in equilibrium in a horizontal position.
A particle of mass pm kg is attached to the beam at A and the beam remains in equilibrium in a horizontal position.
The beam is modelled as a uniform rod.
(a) Given that the tension in the rope attached at C is four times the tension in the rope attached at D, use the model to find the exact value of p. [7]
The particle of mass pm kg at A is removed and replaced by a particle of mass qm kg at A. The beam remains in equilibrium in a horizontal position but is now on the point of tilting.
(b) Using the model, find the exact value of q [4]
(c) State how you have used the modelling assumption that the beam is uniform. [1]

Question 5
speed (m s^–1)
[Diagram or table: see page 12 of the paper]
The speed-time graph in Figure 2 illustrates the motion of a car travelling along a straight horizontal road. At time t = 0 , the car starts from rest and accelerates uniformly for 30 s until it reaches a speed of V m s^–1 The car then travels at a constant speed of V m s^–1 until time t = T seconds.
(a) Show that the distance travelled by the car between t = 0 and t = T seconds is V (T – 15) metres. [2]
A motorbike also travels along the same road.
• The motorbike starts from rest at time t = 10 s and accelerates uniformly for 40 s
• The acceleration of the motorbike is the same as the acceleration of the car
• The motorbike then travels at a constant speed for a further 10 s before decelerating uniformly until it reaches a speed of V m s^–1 at time T seconds
(b) On Figure 2, sketch a speed-time graph for the motion of the motorbike.
[If you need to redraw your sketch, there is a copy of Figure 2 on page 15.] [2]
(c) Show that the constant speed of the motorbike is 4V/3 m s^–1 [2]
At time t = T seconds, the distance travelled by each vehicle is the same.
(d) Find the value of T [5]
[Diagram or table: see page 15 of the paper]

Question 6
[Diagram or table: see page 16 of the paper]
A particle of weight W newtons lies at rest on a rough horizontal surface, as shown in Figure 3. A force of magnitude P newtons is applied to the particle.
The force acts at an angle α to the horizontal, where tan α = 4/3
The coefficient of friction between the particle and the surface is 1/4
Given that the particle does not move, show that
[Diagram or table: see page 16 of the paper]
[7]

Question 7
[Diagram or table: see page 18 of the paper]
A car of mass 1200 kg is towing a trailer of mass 600 kg up a straight road, as shown in Figure 4.
The road is inclined at an angle α to the horizontal, where sin α = 1/12
The driving force produced by the engine of the car is 3000 N.
The car moves with acceleration 0.75 m s^–2
The non-gravitational resistance to motion of
• the car is modelled as a constant force of magnitude 2R newtons
• the trailer is modelled as a constant force of magnitude R newtons
The car and the trailer are modelled as particles. The tow bar between the car and trailer is modelled as a light rod that is parallel to the direction of motion.
Using the model,
(a) show that the value of R is 60 [4]
(b) find the tension in the tow bar. [3]
When the car and trailer are moving at a speed of 12 m s^–1 , the tow bar breaks.
Given that the non-gravitational resistance to motion of the trailer remains unchanged,
(c) use the model to find the further distance moved by the trailer before it first comes to rest. [4]

Question 8
[Diagram or table: see page 22 of the paper]
A square floor space ABCD, with centre O, is modelled as a flat horizontal surface measuring 50 m by 50 m, as shown in Figure 5. → → The horizontal unit vectors i and j are in the direction of AB and AD respectively.
All position vectors are given relative to O.
A small robot R is programmed to travel across the floor at a constant velocity.
• At time t = 0 , R is at the point with position vector (–2i + j) m
• At time t = 11 s , R is at the point with position vector (9i + 23j) m
• At time t seconds, the position vector of R is r metres
(a) Find, in terms of t, i and j, an expression for r [3]
A second robot S is at the point C.
• At time t = 0 , S leaves C and moves with constant velocity (–i – j) m s^–1
• At time t seconds, the position vector of S is s metres
(b) Write down, in terms of t, i and j, an expression for s [1]
(c) Show that
[Diagram or table: see page 22 of the paper]
[2]
(d) Find the time when the distance between R and S is a minimum. [3]