Candidate surname Other names
Centre Number Candidate Number
Afternoon
Mathematics
� �
Advanced
PAPER 32: Mechanics
Marks
Candidates may use any calculator allowed 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).
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.
Unless otherwise indicated, whenever a value of g is required, take g = 9.8 m s−2 and
give your answer to either 2 significant figures or 3 significant figures.
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 50. There are 6 questions.
– use this as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. A car moves in a straight line along a horizontal road with constant acceleration 2 m s–2
The car is moving with speed 15 m s–1 in the direction of the acceleration when it passes
a signpost on the road.
The car is modelled as a particle.
(a) Use the model to find the speed of the car 4 s after passing the signpost.
(2)
Figure 1 below shows the horizontal forces acting on the car.
Given that
• the car has mass 800 kg
• the driving force of the engine has magnitude D newtons
• the resistance to the motion of the car has magnitude 400 N
• the acceleration of the car is 2 m s–2 in the direction of the driving force
(b) use the model to find the value of D.
(2)
2 m s–2
400 N DN
800 kg
Figure 1
2
■■■■
,Question 1 continued
(Total for Question 1 is 4 marks)
3
■■■■ Turn over
, 2.
5N
B (2 kg)
α
Figure 2
A small box B of mass 2 kg is dragged in a straight line, along a rough horizontal plane,
at a constant speed by a force of magnitude 5 N.
3
The line of action of the force makes an angle α with the plane, where sin α = ,
5
as shown in Figure 2.
(a) Show that the magnitude of the normal reaction of the plane on the box is 16.6 N.
(3)
At the instant when B is at the point O on the plane, the force of magnitude 5 N
is removed.
(b) Describe the motion of the box after the force of magnitude 5 N is removed.
(1)
(c) Find the magnitude of the normal reaction of the plane on the box after the force of
magnitude 5 N is removed.
(1)
Given that after the force of magnitude 5 N is removed
• the box is modelled as a particle
• air resistance is modelled as being negligible
• the coefficient of friction between the box and the plane is modelled as 0.2
• the speed of the box as it passes through O is 4 m s–1
• the box comes to rest at the point X on the plane
(d) use the model to find the length OX.
(4)
(e) State one limitation of the model, apart from ignoring air resistance, that could affect
your answer to part (d).
(1)
4
■■■■
Centre Number Candidate Number
Afternoon
Mathematics
� �
Advanced
PAPER 32: Mechanics
Marks
Candidates may use any calculator allowed 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).
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.
Unless otherwise indicated, whenever a value of g is required, take g = 9.8 m s−2 and
give your answer to either 2 significant figures or 3 significant figures.
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 50. There are 6 questions.
– use this as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. A car moves in a straight line along a horizontal road with constant acceleration 2 m s–2
The car is moving with speed 15 m s–1 in the direction of the acceleration when it passes
a signpost on the road.
The car is modelled as a particle.
(a) Use the model to find the speed of the car 4 s after passing the signpost.
(2)
Figure 1 below shows the horizontal forces acting on the car.
Given that
• the car has mass 800 kg
• the driving force of the engine has magnitude D newtons
• the resistance to the motion of the car has magnitude 400 N
• the acceleration of the car is 2 m s–2 in the direction of the driving force
(b) use the model to find the value of D.
(2)
2 m s–2
400 N DN
800 kg
Figure 1
2
■■■■
,Question 1 continued
(Total for Question 1 is 4 marks)
3
■■■■ Turn over
, 2.
5N
B (2 kg)
α
Figure 2
A small box B of mass 2 kg is dragged in a straight line, along a rough horizontal plane,
at a constant speed by a force of magnitude 5 N.
3
The line of action of the force makes an angle α with the plane, where sin α = ,
5
as shown in Figure 2.
(a) Show that the magnitude of the normal reaction of the plane on the box is 16.6 N.
(3)
At the instant when B is at the point O on the plane, the force of magnitude 5 N
is removed.
(b) Describe the motion of the box after the force of magnitude 5 N is removed.
(1)
(c) Find the magnitude of the normal reaction of the plane on the box after the force of
magnitude 5 N is removed.
(1)
Given that after the force of magnitude 5 N is removed
• the box is modelled as a particle
• air resistance is modelled as being negligible
• the coefficient of friction between the box and the plane is modelled as 0.2
• the speed of the box as it passes through O is 4 m s–1
• the box comes to rest at the point X on the plane
(d) use the model to find the length OX.
(4)
(e) State one limitation of the model, apart from ignoring air resistance, that could affect
your answer to part (d).
(1)
4
■■■■
