Marr College Physics
Higher Physics
Our Dynamic Universe - Homework
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Home learning is a vital part of your education
The following will have a positive impact on your learning, progress
and overall level of attainment
– Spending at least the same amount of time and care on
homework questions that you would in class
– Completing all questions to the best of your ability for the due
date
– Answering the questions with your notes beside you to consult
if you are stuck
– Using the time between homework being issued and hand-in to
ask your teacher for help
– Self-assessing using the numerical answers provided
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If you get the same answer as the file, you feel good and your confidence
develops
If you get a different answer, it allows you to go back and look at your working
and try to spot and correct mistakes
If you still can’t see what is wrong, ask your teacher
– Responding positively to feedback provided by your teacher
and using the advice to improve
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Relationships Required for Higher Physics
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3
Homework 1 - Significant Figures, Prefixes & Scientific
Notation
1. In each of the following cases, the stated value has too many significant figures.
The appropriate number of significant figures is stated in brackets after the
quantity. Round each quantity to the correct number of significant figures.
a)
b)
c)
d)
11.85467 V
50.7835 Hz
0.000000712 m
2.998 x 108 ms-1
(3 significant figures)
(2 significant figures)
(3 significant figures)
(2 significant figures)
2. Calculate the following quantities from the information given, and report your
answer to an appropriate number of significant figures. Remember to give your
answer in scientific notation!
a) Calculate the frequency of microwaves that have a wavelength of
3.1 x 10-2 m, and are travelling at 3.0 x 108 ms-1.
b) Calculate the energy used if a 1.2 kW kettle takes 2 minutes to boil.
3. Copy the table below, and fill in all the blanks.
QUANTITY
Speed of light
Charge on an electron
Wavelength of red light
Voltage used in the
Super Grid
VALUE
SCIENTIFIC NOTATION
3 x 108 ms-1
0.000 000 000 000 000
000 160 C
7 x 10-7 m
250 000 V (to 3 sig figs)
4. Re-write the following quantities using the most appropriate prefix.
a) 0.000 006 m
b) 1 500 000 000 Hz
c) 3200 W
d) 0.008 g
e) 2.7 x 106 J
f) 7.42 x 10-7 m
4
Homework 2 - Uncertainties
1. The circuit shown is set up to determine the resistance of a resistor. In one
repetition of the experiment, the readings are as shown on the meters. The
experiment is repeated several times to allow mean values for both current and
voltage to be found.
0
1
2
3
V
0
0.
2
0.
4
0.
6
A
a) Give the ammeter and voltmeter readings and state the scale reading uncertainty
in each case.
b) Using Ohm’s Law (V = IR), calculate a value for the resistor. Estimate the absolute
uncertainty in the calculated value of the resistance and explain how you arrived at
your estimate.
c) The experiment is repeated 5 times, and the values recorded for the current are as
follows:
0.44 A; 0.43 A; 0.45 A; 0.42 A; 0.44 A
Calculate the mean current, and the random uncertainty in the mean.
2. A current is measured with an analogue meter which has scale divisions of 0.1 A,
and is found to be 5.4 A. The reading is double-checked with a digital meter, and
again is found to be 5.4 A. Using which instrument gives the larger scale reading
uncertainty? Explain your answer.
5
Homework 3 - Vectors
1. Physical quantities can be classified as scalar or vector.
(a) Explain the difference between a scalar and a vector quantity
(b) Provide 2 examples of a scalar quantity
(c) Provide 2 examples of a vector quantity.
2. A ferry crosses a river that is flowing at 5 ms-1.
If the ferry is travelling at 12 ms-1, calculate
its resultant velocity.
5 ms-1
12 ms-1
3. An aircraft pilot wishes to fly north at 800 km h-1. A wind is blowing at 80 km h-1
from west to east. What speed and course must he select in order to fly the
desired course?
4. A footballer runs around a football pitch as part of his training. He starts at the
halfway line (point X), and runs around the pitch to point D as shown. This run
100 m
takes him 50 seconds.
C
B
N
70 m
70 m
W
E
S
D
X
50 m
A
a) Calculate the total distance travelled by the footballer.
b) What is his final displacement at point D?
c) Calculate the footballer’s average velocity for the run.
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Homework 4 - Equations Of Motion
1. A labourer on scaffolding outside one of the physics classrooms drops
a wrench. A student times it as it falls past the 2m tall classroom window and
found that it took 0.6s to fall . Calculate the wrench’s initial velocity as it
appears at the top of the window.
2. A train decelerates from 12.0 ms-1 to 5.0 ms-1 while travelling a distance of
119.0 m along a straight track. Calculate the deceleration of the train.
3. A skier sets off from rest and accelerates uniformly down a straight ski run.
After 4·50 seconds she reaches a speed of 23·0 m s-1. After this time the skier no
longer accelerates but continues to travel at 23·0 m s-1 for a further 11·0 s.
Calculate:
a) the acceleration of the skier during the first 4·50 s of her run.
b) the total distance travelled by the skier.
4. In a staggered sprint race, sprinters P and Q both start the race at the same time
but from different starting positions on the track.
The stagger is such that both sprinters reach XY, as shown below, at the same
time.
Sprinter P has a constant acceleration of 1.6 ms-2 from the start line to the line
XY. Sprinter Q has a constant acceleration of 1.2 ms-2 from the start line to XY.
a) Calculate the time taken by the sprinters to reach line XY.
b) Find the speed of each sprinter at this line.
c) What is the distance, in metres, between the starting lines for
sprinters P and Q?
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Homework 5 - Forces
1. A train made up of the engine and 2 carriages is pulled along a level track by a
force of 16 500 N. The engine has a mass of 8 000 kg. Each of the carriages has
a mass of 8 000 kg. The engine experiences a frictional force of 1500 N and the
carriages both also experience 1500 N each.
Force
applied by
the engine
B
A
a) Calculate the acceleration of the train.
b) Work out the tension in link B.
2. A rocket of mass 200 kg accelerates vertically upwards from the surface of a
planet at 2ms-2. The gravitational field strength on the planet is 4 Nkg-1.
What is the size of the force being supplied by the rocket’s engines?
3. The lift in a department store has a mass of 1100kg.
The lift is descending with a uniform downwards
acceleration of 2ms-2. The acceleration due to gravity
can be taken as 10ms-2.
What is the force applied to the lift by the lift cable?
4. A pupil pushes two blocks A and B with a 30 N force.
4kg
A
2kg
B
Ignoring friction,
a) calculate the acceleration of the blocks.
b) find the force A exerts on B.
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Homework 6 – Force as a Vector
1. In the diagram below, calculate the component of the weight acting down the
slope. The mass of the trolley is 24 kg.
30o
2. A 2 kg trolley is placed on a 35o slope. The trolley accelerates down the slope and
a frictional force of 1.5 N acts up the slope.
1.5 N
35o
a) Calculate the acceleration of the trolley.
b) What effect does increasing the angle of slope have on acceleration?
Assume that the frictional force remains constant.
3. Two ropes are used to pull a boat at constant speed along a canal.
Each rope exerts a force of 150 N at 20o to the direction of travel of the boat as
shown.
a) Calculate the magnitude of the resultant force exerted by the ropes.
b) What is the magnitude of the frictional forces acting on the boat?
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Homework 7 – Conservation of Energy
1. A block of mass 3·0 kg is held at rest on a frictionless slope. The front edge of the
block is 0·80 m above the ground as shown in Figure 2.
a) Calculate the gain in gravitational potential energy of the block when it is
in theposition shown in Figure 2.
b) The block is released. Use conservation of energy to find the speed of the
block at the foot of the slope.
2. In an experiment to calculate the power developed , a 70 kg man runs up the
stairs as fast as he can. The flight of stairs is 4.30 m tall.
If it took the man 5.0 s to run up the stairs, calculate
his power.
3. A pendulum swings as shown in the diagram.
Points A and C are the extremities of the
swing of the pendulum. The mass of the
bob is 0.5 kg. Calculate:
20 cm
a) the maximum potential energy of the bob.
b) the maximum kinetic energy of the bob.
c) the maximum speed of the bob.
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Homework 8 – Momentum and impulse
1. In a rugby match, a 110 kg forward in one team tackles
an 85 kg back in the other team. The forward is travelling
at 5 ms-1 and the back at 7 ms-1 in the opposite direction
when they collide and ‘stick’ together.
Take the direction of the forward as the positive direction.
a) Calculate the velocity of the pair immediately after the collision.
b) Show by calculation whether this collision is elastic or inelastic.
3. In a game of squash, a ball of mass 0.1 kg is moving towards the
player with a velocity of 20 ms-1. She strikes it with the racquet
and it returns towards the wall at 40 ms-1. If the time of contact
between racquet and ball is 50 ms, calculate the force applied on
the ball by the racquet.
4. A golfer strikes a stationary golf ball of mass 0.1 kg.
The force applied by the club on the ball varies with time as shown in the graph
below.
Average
Force / N
160
120
80
40
0
20
40
60
80
Time of
contact / ms
(a) (i) Use this graph to determine the impulse given to the ball.
(ii) Calculate the speed that the ball leaves the club with.
(b) The golfer uses a softer ball.
Copy the graph above and on the same graph show the variation of force with
time for the softer ball.
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Homework 9 - Gravitation
1. During a visit to the moon, the astronaut fires a small experimental projectile
across a level surface. The projectile is launched, from point P, at a speed of 24.0
ms-1 and at an angle of 60° to the horizontal.
The projectile lands 26.0 s later at point X.
a)
b)
Calculate the horizontal speed of the projectile at point P.
Calculate the horizontal distance from P to X.
2. A model rocket enthusiast launches a rocket from the edge of a cliff on a calm day
(no air resistance).
O
30O
A
B
The flight of the rocket from launch at point O to splashdown in the sea, at B,
takes 7 seconds.
a) The rocket is launched at an angle of 30O to the ground with velocity
40ms-1.
Show that the time it takes to go from point O to point A, which is level
with the cliff, is 41s.
b) Find the height of the cliff.
3. Calculate the gravitational force between two cars parked 0.50 m apart. The
mass of each car is 1000 kg.
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Homework 10 – Special Relativity
1. The lifetime of a star is 10 billion years as measured by an observer at rest with
respect to the star. The star is moving away from the Earth at a speed of 0·72 c.
Calculate the lifetime of the star according to an observer on the Earth.
2. A spacecraft moving with a constant speed of 0·75 c passes the Earth. An
astronaut on the spacecraft measures the time taken for an athlete to run 100 m.
The astronaut measures this time to be 15.23s. Calculate the athlete’s time as
measured on the Earth.
3. A scientist in the laboratory measures the time taken for a nuclear reaction to
occur in an atom. When the atom is travelling at 8·0 × 107 m s 1 the reaction
takes 3·0 × 104 s. Calculate the time for the reaction to occur when the atom is
at rest.
4. A rocket has a length of 25 m when at rest on the Earth. An observer, at rest on
the Earth, watches the rocket as it passes at a constant speed of 1·7 × 108 m s 1.
Calculate the length of the rocket as measured by the observer.
5. A tau meson is moving at 0·86 c relative to a magnet. The magnet has a length of
1·00 m when at rest to the Earth. Calculate the length of the magnet in the
reference frame of the tau meson.
6. In the year 2050 a spacecraft flies over a base station on the Earth. The spacecraft
has a speed of 0·85 c. The length of the moving spacecraft is measured as 150m
by a person on the Earth. The spacecraft later lands and the same person
measures the length of the now stationary spacecraft. Calculate the length of the
stationary spacecraft.
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Homework 11 – Doppler Effect
1. In the following sentences the words represented by the letters A, B, C and D are
missing:
A moving source emits a sound with frequency fs. When the source is moving
towards a stationary observer, the observer hears a ____A_____ frequency fo.
When the source is moving away from a stationary observer, the observer hears a
____B_____ frequency fo. This is known as the _____C____ ____D_____.
Match each letter with the correct word from the list below:
Doppler
effect
higher
quieter
louder
lower
softer
2. A student is standing on a station platform. A train approaching the station
sounds its horn as it passes through the station. The train is travelling at a speed
of 25 m s 1. The horn has a frequency of 200 Hz.
a) Calculate the frequency heard as the train is approaching the student.
b) Calculate the frequency heard as the train is moving away from the
student.
3. A man standing at the side of the road hears the horn of an approaching car. He
hears a frequency of 470 Hz. The horn on the car has a frequency of 450 Hz.
Calculate the speed of the car.
4. A battery-operated siren emits a constant note of 2200 Hz. It is rotated in a circle
of radius 0·8 m at 3·0 revolutions per second. A stationary observer, standing
some distance away, listens to the note made by the siren.
a) Show that the siren has a constant speed of 15·1 m s 1.
b) Calculate the minimum frequency heard by the observer.
c) Calculate the maximum frequency heard by the observer.
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Homework 12 – Redshift and Hubble’s Law
1. Light from a distant galaxy is found to contain the spectral lines of hydrogen. The
light causing one of these lines has a measured wavelength of 466 nm. When the
same line is observed from a hydrogen source on Earth it has a wavelength of 434
nm.
a) Calculate the Doppler shift, z, for this galaxy.
b) Calculate the speed at which the galaxy is moving relative to the
Earth.
c) In which direction, towards or away from the Earth, is the galaxy
moving?
2. The galaxy Corona Borealis is approximately 1 000 million light years away from
the Earth. Calculate the speed at which Corona Borealis is moving away from the
Earth.
3. A distant quasar is moving away from the Earth. Hydrogen lines are observed
coming from this quasar. One of these lines is measured to be 20 nm longer than the
same line, of wavelength 486 nm from a source on Earth.
a) Show that the speed at which the quasar is moving away from the
Earth is 1.2 x 107 ms-1.
b) Calculate the approximate distance, in millions of light years, that the
quasar is from the Earth.
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Exam-standard Exercises
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Each of these exercises consist of both multiple choice and long answer
questions.
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All of these questions are of the same standard as those in the final exam.
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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
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Numerical answers are provided – therefore you should be able to self-assess
• Check your answers, spot mistakes and fix
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You are therefore expected to attempt and complete all questions and hand in
for the agreed deadline
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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.
25
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.
26
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.
27
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.
28
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 108 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.
30
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 .
31
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
32
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.
33
6.
34
Numerical Answers
Exercise 1
1. (a ) 11.86 V
(b) 51 Hz
(c) 7.12 x 10-7m
(d) 3.0 x 108 m s-1
2. (a) 9.7 x 109 Hz
(b) 1 x 105 J
4. (a) 6 m
(b) 1.5 GHz
(c) 3.2 kW
(d) 8 mg
(e) 2.7 MJ
(f) 742 nm
Exercise 2
1. (b) (2.7  0.2) 
(c) mean 0.44 A
random uncertainty = 0.006 A = 0.01 A
Exercise 3
2. 13 m s-1 at 113
3. 804 m s-1 at 354
4. (a) 290 m
(b) 50 m at 270
(c) 1 m s-1 at 270
Exercise 4
1. 0.393 m s -1
2. 0.5 m s-2
3. (a) 5.11 m s-2
(b) 305 m
4. (a) 5 s
(b) P: 8 m s-1, Q: 6 m s-1
(c) 5 m
35
Numerical answers
Exercise 5
1. (a) 0.5 m s-2
(b) 5500 N
2. 1200 N
3. 8580 N
4. (a) 5 m s-2
(b) 10 N
Exercise 6
1. 118 N
2. (a) 4.87 m s-2
3. (a) 282 N
(b) 282 N
Exercise 7
1. (a) 23.52 J
(b) 3.96 m s-1
2. 590 W
3. (a) 0.98 J
(b) 0.98 J
(c) 1.98 m s-1
Exercise 8
1. (a) 0.23 m s-1 in original direction of “back”
(b) Ek before = 3457.5 J, Ek after = 5.16 J
2. 120 N
3. (a) (i) 4.8 Ns
(ii) 48 m s-1
36
Numerical answers
Exercise 5
1. (a) 0.5 m s-2
(b) 5500 N
2. 1200 N
3. 8580 N
4. (a) 5 m s-2
(b) 10 N
Exercise 6
1. 118 N
2. (a) 4.87 m s-2
3. (a) 282 N
(b) 282 N
Exercise 7
1. (a) 23.52 J
(b) 3.96 m s-1
2. 590 W
3. (a) 0.98 J
(b) 0.98 J
(c) 1.98 m s-1
Exercise 8
1. (a) 0.23 m s-1 in original direction of “back”
(b) Ek before = 3457.5 J, Ek after = 5.16 J
2. 120 N
3. (a) (i) 4.8 Ns
(ii) 48 m s-1
37
Numerical answers
Exercise 9
1. (a) 12 m s-1
(b) 312 m
2. (a) 0.41 s
(b) 99.2 m
3. 2.7 x 10-4 N
Exercise 10
1. 14.4 billion years
2. 10.1 s
3. 2.9 x 10-4 s
4. 21 m
5. 0.26 m
6. 285 m
Exercise 11
2. (a) 216 Hz
(b) 186 Hz
3. 14.4 m s-1
4. (a) 15.1 m s-1
(b) 2106 Hz
(c) 2302 Hz
Exercise 12
1. (a) 0.07
(b) 2.1 x 107 m s-1
2. 2.2 x 107 m s-1
3. (a) 1.2 x 107 m s-1
(b) 5.2 x 1024 m
38
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
39
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
40