Exam-standard Exercises
•
Each of these exercises consist of both multiple choice and long answer
questions.
•
All of these questions are of the same standard as those in the final exam.
•
Your teacher will issue these at the end of each key area(s) and give you plenty
of time to complete the questions
•
You are also able to ask for help before the hand-in date
•
Numerical answers are provided – therefore you should be able to self-assess
• Check your answers, spot mistakes and fix
•
You are therefore expected to attempt and complete all questions and hand in
for the agreed deadline
1
Relationships Required for Higher Physics
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3
Exam Standard Exercise A: Motion – Equations and Graphs
1. A student sets up the apparatus in the diagram to measure the average
acceleration of a model car as it travels from P to Q.
For one run, the following measurements were recorded along with their
estimated errors:
clock 1 reading
clock 2 reading
stopwatch reading
length of car
distance PQ
= (0.23 ± 0.01) s
= (0.12 ± 0.01) s
= (0.95 ± 0.20) s
= (0.050 ± 0.0002) m
= (0.30 ± 0.01) m
The measurement which gives the largest percentage uncertainty is the
A
B
C
D
E
reading on clock 1
reading on clock 2
reading on the stopwatch
length of car
distance PQ
2. A car accelerates uniformly from rest and travels a distance of 60 m in 6 s. The
acceleration of the car, in ms-2, is
A
B
C
D
E
0.83
3.3
5.0
10
20
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3. Consider the following three statements made by pupils about scalars and
vectors.
I
II
III
Scalars have direction only.
Vectors have both size and direction.
Speed is a scalar and velocity is a vector.
Which statement(s) is/are true?
A
B
C
D
E
I only
I and II only
I and III only
II and III only
I, II and III only
4. A stunt motorcyclist attempts to jump a river which is 5 m wide. The bank from
which he will take off is 2 m higher than the bank on which he will land as
shown below.
What is the minimum horizontal speed he must achieve just before take-off to
avoid landing in the river?
A
B
C
D
E
2.0 ms-1
3.2 ms-1
7.9 ms-2
10.0 ms-1
12.5 ms-1
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5. A ball is thrown vertically upwards from ground level. When it falls to the
ground, it bounces several times before coming to rest. Which one of the
following velocity-time graphs represents the motion of the ball from the
instant it leaves the thrower’s hand until it hits the ground for a second time.
A
B
C
D
E
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6. The manufacturers of tennis balls require that the balls meet a given standard.
When dropped from a certain height onto a test surface, the balls must rebound
to within a limited range of heights.
The ideal ball is one which, when dropped from rest from a height of 3.15 m,
rebounds to a height of 1.75 m as shown below.
a)
Assuming air resistance is negligible, calculate
(i) the speed of an ideal ball just before contact with the ground
(ii) the speed of this ball just after contact with the ground.
b)
When a ball is tested six times, the rebound heights are measured to
be
1.71 m, 1.78 m, 1.72 m, 1.76 m, 1.73 m, 1.74 m
Calculate
(i) the mean value of the height of the bounce
(ii) the random uncertainty in the mean value.
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7. In an orienteering event, competitors navigate from the start to control points
around a set course.
Two orienteers, Andy and Paul, take place in a race in a flat area. Andy can run
faster than Paul, but Paul is a better navigator.
From the start, Andy runs 700 m north (000) then 700 m south-east (135) to
arrive at the first control point. He has an average running speed of 3 ms -1.
a)
By scale drawing or otherwise, find the displacement of Andy, from the
starting point, when he reaches the first control point.
b)
Calculate the average velocity of Andy between the start and the first
control point.
c)
Paul runs directly from the start to the first control point with an average
running speed of 2.5 ms-1.
Determine the average velocity of Paul.
d)
Paul leaves the starting point 5 minutes after Andy.
Show by calculation who is first to arrive at this control point.
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8. a)
b)
A sports car is being tested along a straight track.
(i)
In the first test, the car starts from rest and has a constant
acceleration of 4.0 ms-2 in a straight line for 7.0 s.
Calculate the distance the car travels in 7.0 s.
(ii)
In a second test, the car again starts from rest and accelerates at
4.0 ms-2 over twice the distance covered in the first test.
What is the increase in the final speed of the car at the end of the
second test compared with the speed at the end of the first test.
(iii)
In a third test, the car reaches a speed of 40 ms-1. It then
decelerates at 2.5 ms-2 until it comes to rest.
Calculate the distance travelled by the car while it decelerates to
rest.
A student measures the acceleration of a trolley as it moves freely down a
sloping track.
The trolley has a card mounted on it. As it moves down the track the card
cuts off the light at each of the light gates in turn. Both the light gates are
connected to the computer which is used for timing.
The student uses a stopclock to measure the time it takes the trolley to
move from the first light gate to the second light gate.
(i)
(ii)
List all of the measurements that have to be made by the student
and the computer to allow the acceleration of the trolley to be
calculated.
Explain fully how each of these measurements is used in
calculating the acceleration of the trolley as it moves down the
slope.
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Exam Standard Exercise B: Forces, energy and power
1. A force of 15 N acts on a box as shown below.
Which entry in the following table correctly shows the horizontal and vertical
components of the force?
Horizontal component
(N)
Vertical component
(N)
A
15 sin 60°
15 sin 30°
B
15 cos 60°
15 sin 30°
C
15 sin 60°
15 cos 60°
D
15 cos 30°
15 sin 30°
E
15 cos 60°
15 sin 60°
2. A block of weight 1500 N is dragged along a horizontal road at constant speed by
a force of 500 N.
What is the frictional force between the block and the road?
A
B
C
D
E
3N
500 N
1000 N
1500 N
2000 N
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3. A block of wood, of mass 2.0 kg, slides with a constant velocity down a slope.
The slope makes an angle of 30° with the horizontal as shown in the diagram.
What is the value of the force of friction acting on the block.
A
B
C
D
E
1.0 N
1.7 N
9.8 N
17.0 N
19.6 N
4. A car of mass 900 kg pulls a caravan of mass 400 kg along a straight horizontal
road with an acceleration of 2 ms-2.
Assuming that the frictional forces are negligible, the tension in the coupling
between the car and caravan is
A
B
C
D
E
400 N
500 N
800 N
1800 N
2600 N
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5. a)
A hot air balloon, of total mass 500 kg, is held stationary by a single vertical
rope.
(i) Draw a sketch of the balloon. On your sketch, mark and label all the
forces acting on the balloon.
(ii) When the rope is released, the balloon initially accelerates vertically
upwards at 1.5 ms-2. Find the magnitude of the buoyancy force.
(iii) Calculate the tension in the rope before it is released.
b)
An identical balloon is moored using two ropes, each of which makes an
angle of 25° to the vertical, as shown below.
By using a scale diagram, or otherwise, calculate the tension in each rope.
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6. During a test on car safety, two cars are crashed together on a test track.
a)
Car A, which has a mass of 1200 kg and is moving at 18.0 ms-1, approaches
car B, which has a mass of 1000 kg and is moving at 10.8 ms-1, in the
opposite direction.
The cars collide head on, lock together and move off in the direction of
car A.
(i) Calculate the speed of the cars immediately after the collision.
(ii) Show by calculation that this collision is inelastic.
b)
During a second safety test, a dummy in a car is used to demonstrate the
effects of a collision.
During the collision, the head of the dummy strikes the dashboard at
20 ms-1 as shown below and comes to rest in 0.02 s.
The mass of the head is 5 kg.
(i) Calculate the average force exerted by the dashboard on the head of
the dummy during the collision.
(ii) The test on the dummy is repeated with an airbag which inflates during
the collision.
During the collision, the head of the dummy again travels forward at
20 ms-1 and is brought to rest by the airbag.
Explain why there is less risk of damage to the head of the dummy
when the airbag is used.
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7. A child on a sledge slides down a slope which is at an angle of 20° to the
horizontal as shown below.
The combined weight of the child and the slope is 400 N. The frictional force
acting on the sledge and child at the start of the slide is 20.0 N.
a)
(i) Calculate the component of the combined weight of the child and
sledge down the slope.
(ii) Calculate the initial acceleration of the sledge and child.
b)
The child decides to start the slide from further up the slope. Explain
whether or not this has any effect on the initial acceleration.
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8. A student performs an experiment to study the motion of the school lift as it
moves upwards.
The student stands on bathroom scales during the lift’s journey upwards.
The student records the reading on the scales at different parts of the lift’s
journey as follows.
Part of journey
Reading on scales
At the start (lift accelerating)
678 N
In the middle (steady speed)
588 N
At the end (lift decelerating)
498 N
a)
Show that the mass of the student is 60 kg.
b)
Calculate the initial acceleration of the lift.
c)
Calculate the deceleration of the lift.
d)
During the journey, the lift accelerates for 1.0 s, moves at a steady speed
for 3.0 s and decelerates for a further 1.0 s before coming to rest.
Sketch the acceleration-time graph for this journey.
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Exam Standard Exercise C: Gravitation
1. An aeroplane is flying at 160 ms-1 in level flight 80 m above the ground. It
releases a package at a horizontal distance X from the target T.
The effect of air resistance can be neglected and the acceleration due to gravity
can be taken at 10 ms-2.
The package will score a direct hit on target t if X is
A
B
C
D
E
40 m
160 m
320 m
640 m
2560 m
2. The distance between the Earth and the Moon is 3.84 x 10 8 m. The mass of the
Earth is 5.98 x 1024kg and the mass of the moon is 7.35 x 1022 kg. The gravitational
force between the Earth and the Moon is
A
B
C
D
E
2.74 x 10-3 N
1.99 x 1020 N
7.63 x 1028 N
2.98 x 1030 N
1.14 x 1039 N
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3. The fairway on a golf course is in two horizontal parts separated by a steep bank
as shown below.
A golf ball at point O is given an initial velocity of 41.7 ms-1 at 36° to the
horizontal.
The ball reaches a maximum vertical height at point P above the upper fairway.
Point P is 19.6 m above the upper fairway as shown. The ball hits the ground at
point Q.
The effect of air friction on the ball may be neglected.
a)
Calculate
(i) the horizontal component of the initial velocity of the ball;
(ii) the vertical component of the initial velocity of the ball.
b)
Show that the time taken for the ball to travel from point O to point Q
is 4.5 s.
c)
Calculate the horizontal distance travelled by the ball.
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4. A Russian Soyuz rocket has launched from French Guiana to put six satellites in
orbit.
One satellite, Pleiades-1, is designed to produce pictures that resolve features
on the ground as small as 50 cm across.
Lift-off occurred on schedule at 23.03 local time, Friday 16 December 2011 with
Pleiades-1 being dropped off in its 700 km high polar orbit some 55 minutes
later. The 970 kg satellite is the result of a near-decade-long programme in the
French space agency (CNES) to develop one of the most powerful Earth
observation systems in the world.
(Mass of the Earth = 5.98 x 1024kg)
(Radius of Earth = 6.4 x 106 m)
a)
State Newton’s Law of Gravitation.
b)
Calculate the size of the gravitational force on the satellite in its orbit.
(Hint – ‘r’ in Newton’s Law of Gravitation is distance of satellite from centre
of Earth).
c)
Calculate the size of the gravitational field strength in this orbit .
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Exam Standard Exercise D: Special relativity and
expanding Universe
1. The siren on a fire engine has a frequency of 260 Hz. The fire engine is
moving away from a stationary observer at 10 m s-1. The frequency heard
by the observer is
A 235 Hz
B 253 Hz
C
260 Hz
D 268 Hz
E
291 Hz
2. A pupil makes the following statements about a star receding from Earth.
I
II
III
The light from a star will be red shifted.
The light from the star will be shifted to a longer wavelength.
The light from the star is shifted to a lower frequency.
Which statement(s) is/are correct?
A
B
C
D
E
I only
II only
III only
I and II only
I, II and III only
3. The universe has constantly cooled down as it expands. The temperature
of the universe can be calculated by measuring the peak wavelength of
background
A
B
C
D
E
Infra Red
Radio waves
Ultra Violet
Microwaves
X – rays
4. A starship at rest is 12 m long. The starship then travels past a stationary
observer at 0.8c. How long does the starship appear to be to the observer
when in motion.
A
B
C
D
E
7.2 m
12 m
13.5 m
16.4 m
15.2 m
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5. In ‘Star Trek’ the spaceship U.S.S. Enterprise travels at 0.25c using impulse
power. The spaceship is 725 m long.
a)
Calculate what length a stationary observer on the planet Vulcan would
view the ship to be.
b)
The ship emits a light flare of wavelength 500 nm. What wavelength
would the stationary observer view when the ship was moving away
from them at 2.0 x107 m s-1 ?
c)
The crew of the U.S.S. Enterprise observe a galaxy receding from the ship
at 2.5 x106 ms-1. Calculate how far away from the ship the galaxy is.
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6.
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Numerical answers
Exam Standard Exercise A
6. (a) (i) 7.86 m s-1
(ii) 5.86 m s-1
(b) (i) 1.74 m
(ii) 0.01 m
7. (a) 550 m at 069
(b) 1.18 m s-1 at 069
(c) 2.5 m s-1at 069
(d) Andy’s time = 467 s, Paul’s time = 520 s
8. (a) (i) 98 m
(ii) 39.6 m s-1
(iii) 320 m
Exam Standard Exercise B
5. (a) (ii) 5650 N
(iii) 750 N
(b) 414 N
6. (a) (i) 4.9 m s-1
(ii) Ek before = 252 720 J, Ek after = 26 411 J
(b) (i) 5000 N
7. (a) (i) 137 N
(ii) 2.87 m s-2
8. (a) 60 kg
(b) 1.5 m s-2 upwards
(c) deceleration = 1.5 m s-2
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Numerical answers
Exam Standard Exercise C
3. (a) (i) 33.7 m s-1
(ii) 24.5 m s-1
(c) 152 m
4. (b) 7675 N
(c) 7.9 N kg-1
Exam Standard Exercise D
5. (a) 702 m
(b) 533 nm
(c) 1.1 x 1024 m
6. (b) 1.7
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