100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Compilation Booklet of Past Papers for Mechanics Paper 4 £4.27
Add to cart
Quickly navigate to
Preview
  2.  
  3. CIE
  4.  
  5. Mathematics
  6.  
  7. Unit 4 - Mechanics 1

Exam (elaborations)

Compilation Booklet of Past Papers for Mechanics Paper 4
 13 views  0 purchase
  • Institution
  • CIE

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

Preview 10 out of 570  pages

Document information

  • January 25, 2023
  • 570
  • 2022/2023
  • Exam (elaborations)
  • Answers

Subjects

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

More summaries for

All for this textbook (2)

Written for

All documents for this subject (1)

Seller

avatar-seller
SKH392

Reviews received

Content preview

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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


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

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


(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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................



© 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]

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© 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]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................


© UCLES 2016 9709/04/SP/17

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller SKH392. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for £4.27. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

50155 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now

Start selling
£4.27
  • (0)
Add to cart
Added