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Compilation Booklet of Past Papers for Mechanics Paper 4
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Cambridge International AS & A Level Mathematics 9709: Mechanics - Paper 4 Compilation of all past papers for paper 4 from 2019 to 2022

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  • January 25, 2023
  • 570
  • 2022/2023
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Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level




CANDIDATE
NAME

CENTRE CANDIDATE
*0123456789*




NUMBER NUMBER


MATHEMATICS 9709/04
Paper 4 Mechanics 1 (M1) For Examination from 2017
SPECIMEN PAPER 1 hour 15 minutes
Candidates answer on the Question Paper.
Additional Materials: List of Formulae (MF9)

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name in the spaces at the top of this page.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.

Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
Where a numerical value for the acceleration due to gravity is needed, use 10 m s−2 .
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.

At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.




This document consists of 11 printed pages and 1 blank page.


© UCLES 2016 [Turn over

, 2

1 A weightlifter performs an exercise in which he raises a mass of 200 kg from rest vertically through a
distance of 0.7 m and holds it at that height.

(i) Find the work done by the weightlifter. [2]

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(ii) Given that the time taken to raise the mass is 1.2 s, find the average power developed by the
weightlifter. [2]

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© UCLES 2016 9709/04/SP/17

, 3

2 A particle of mass 0.5 kg starts from rest and slides down a line of greatest slope of a smooth plane.
The plane is inclined at an angle of 30Å to the horizontal.

(i) Find the time taken for the particle to reach a speed of 2.5 m s−1 . [3]

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When the particle has travelled 3 m down the slope from its starting point, it reaches rough horizontal
ground at the bottom of the slope. The frictional force acting on the particle is 1 N.

(ii) Find the distance that the particle travels along the ground before it comes to rest. [3]

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© UCLES 2016 9709/04/SP/17 [Turn over

, 4

3 A lorry of mass 24 000 kg is travelling up a hill which is inclined at 3Å to the horizontal. The power
developed by the lorry’s engine is constant, and there is a constant resistance to motion of 3200 N.

(i) When the speed of the lorry is 25 m s−1 , its acceleration is 0.2 m s−2 . Find the power developed
by the lorry’s engine. [4]

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(ii) Find the steady speed at which the lorry moves up the hill if the power is 500 kW and the
resistance remains 3200 N. [2]

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© UCLES 2016 9709/04/SP/17

, 5

4




P
Q


35Å


Blocks P and Q, of mass m kg and 5 kg respectively, are attached to the ends of a light inextensible
string. The string passes over a small smooth pulley which is fixed at the top of a rough plane inclined
at 35Å to the horizontal. Block P is at rest on the plane and block Q hangs vertically below the pulley
(see diagram). The coefficient of friction between block P and the plane is 0.2. Find the set of values
of m for which the two blocks remain at rest. [6]

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© UCLES 2016 9709/04/SP/17 [Turn over

, 6

5
FN


70° 20 N
A B
30° Q 15°
RN
10 N

A small bead Q can move freely along a smooth horizontal straight wire AB of length 3 m. Three
horizontal forces of magnitudes F N, 10 N and 20 N act on the bead in the directions shown in the
diagram. The magnitude of the resultant of the three forces is R N in the direction shown in the
diagram.

(i) Find the values of F and R. [5]

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© UCLES 2016 9709/04/SP/17

, 7

(ii) Initially the bead is at rest at A. It reaches B with a speed of 11.7 m s−1 . Find the mass of the
bead. [3]

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© UCLES 2016 9709/04/SP/17 [Turn over

, 8

6 A particle P moves in a straight line, starting from a point O. The velocity of P, measured in m s−1 ,
at time t s after leaving O is given by

v = 0.6t − 0.03t2 .

(i) Verify that, when t = 5, the particle is 6.25 m from O. Find the acceleration of the particle at this
time. [4]

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© UCLES 2016 9709/04/SP/17

, 9

(ii) Find the values of t at which the particle is travelling at half of its maximum velocity. [6]

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© UCLES 2016 9709/04/SP/17 [Turn over

, 10

7 A cyclist starts from rest at point A and moves in a straight line with acceleration 0.5 m s−2 for a
distance of 36 m. The cyclist then travels at constant speed for 25 s before slowing down, with
constant deceleration, to come to rest at point B. The distance AB is 210 m.

(i) Find the total time that the cyclist takes to travel from A to B. [5]

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© UCLES 2016 9709/04/SP/17

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