Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Friday 19 January 2024
Afternoon (Time: 1 hour 30 minutes) Paper
reference WME03/01
Mathematics
International Advanced Subsidiary/Advanced Level
Mechanics M3
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Yellow), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators must not
have the facility for symbolic algebra manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without working may
•
not gain full credit.
Whenever a numerical value of g is required, take g = 9.8 m s–2, and give your answer to either two
significant figures or three significant figures.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 7 questions in this question paper. The total mark for this paper is 75.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
••
Try to answer every question.
Check your answers if you have time at the end.
If you change your mind about an answer, cross it out and put your new answer and any
working underneath. Turn over
,1. A spacecraft S of mass m moves in a straight line towards the centre, O, of a planet.
The planet is modelled as a fixed sphere of radius R.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The spacecraft S is modelled as a particle.
The gravitational force of the planet is the only force acting on S.
When S is a distance x x R
from O
mgR 2
• the gravitational force is directed towards O and has magnitude
2x2
• the speed of S is v
(a) Show that
gR 2
v2
C
x
where C is a constant.
(3)
When
= x 3=
R, v 3 gR
(b) Find, in terms of g and R, the speed of S as it hits the surface of the planet.
(3)
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2
*P74324A0228*
, Question 1 continued
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A
2l
B
θ
Figure 1
A light elastic spring has natural length l and modulus of elasticity λ
One end of the spring is attached to a point A on a smooth plane.
5
The plane is inclined at angle θ to the horizontal, where tan
12
A particle P of mass m is attached to the other end of the spring.
Initially P is held at the point B on the plane, where AB is a line of greatest slope of
the plane.
The point B is lower than A and AB = 2l, as shown in Figure 1.
The particle is released from rest at B and first comes to instantaneous rest at the point
C on AB, where AC = 0.7l
(a) Use the principle of conservation of mechanical energy to show that
100
mg
91
(5)
(b) Find the acceleration of P when it is released from rest at B.
(4)
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4
*P74324A0428*
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