REVISION PROBLEMS
Speed
1.
The world downhill speed skiing trial takes place at Les Arc every year. Describe a
method that could be used to find the average speed of the skier over the 1km run.
Your description should include:
a) any apparatus required
b) details of what measurements need to be taken
c) an explanation of how you would use the measurements to carry out the
d) calculations.
2.
An athlete ran a 1500 metres race in 3 minutes 40 seconds. Find his average speed for
the race.
3.
How far away is the sun if it takes light 8 minutes to reach Earth?
(Speed of light = 3 × 108 m s-1).
4.
Concorde travels at an average speed of Mach 1.3 between London and New York.
Calculate the time for the journey to the nearest minute. The distance between
London and New York is 4800 km. (Mach 1 is the speed of sound. Take the speed of
sound to be 340 m s-1).
5.
The speed - time graph below represents a girl running for a bus. She starts from a
standstill at O and jumps on the bus at Q.
v/m s-1
t/s
Find:
a)
b)
c)
d)
e)
the steady speed at which she runs
the distance she runs
the increase in the speed of the bus while the girl is on it
how far the bus travels during QR
how far this girl travels during OR.
6.
A ground-to-air guided missile accelerates from rest at 150 m s-2 for 5 seconds. What
speed does it reach?
7.
An Aston Martin accelerated from rest at 6 m s-2. How long does it take to reach a
speed of 30 m s-1 ?
8.
If a family car applies its brakes when travelling at its top speed of 68 m s-1, and
decelerates at 17 m s-2, how long does it take to reduce its speed 34 m s-1?
Answers
Acceleration
9.
An armour-piercing shell, travelling at 2000 m s-1, buries itself in the concrete wall of
a bunker. If it decelerates at 20000 m s-2, what time does it take to come to rest after
striking the wall?
10.
A skateboard running from rest down a concrete path of uniform slope reaches a
speed of 8 m s-1 in 4 s.
What is the acceleration of the skateboard?
How long after it started would the skateboard take to reach a speed of 12 m s-1 ?
11.
In the Tour de France a cyclist is travelling at 20 m s-1. When he reaches a downhill
stretch his speed increases to 40 m s-1. It takes 4 s for him to reach this point on the
hill.
What is the acceleration of the cyclist on the hill?
Assuming he maintains this acceleration, how fast will he be travelling after a further
2s?
How long would it take the cyclist to reach a speed of 55 m s-1 ?
12.
Use the information given below to calculate the acceleration of the trolley.
Length of card = 5 cm
Time on clock 1
Time on clock 2
gate)
Time on clock 3
bottom light gate)
13.
=
=
0.10 s (time taken for card to interrupt top light gate)
0.05 s (time taken for card to interrupt bottom light
=
2.50 s (time taken for trolley to travel between top and
A pupil uses light gates and a suitably interfaced computer to measure the
acceleration of a trolley as it moves down an inclined plane.
The following results were obtained:
acceleration (m s-2) 5.16, 5.24, 5.21, 5.19, 5.20, 5.20, 5.17, 5.19.
Calculate the mean valve of the acceleration and the corresponding random
uncertainty.
Answers
MECHANICS AND PROPERTIES OF MATTER PROBLEMS
Vectors
14.
A car travels 50 km N and then returns 30 km S. The whole journey takes 2 hours.
Calculate: a) the distance travelled
Calculate: b) the average speed
Calculate: c) the displacement
Calculate: d) the average velocity.
15.
A girl delivers newspapers to three houses, ×, Y, Z, as shown in the diagram, starting
at ×. The girl walks directly from one house to the next.
Calculate the total distance the girl walks.
Calculate the girl’s final displacement from ×.
If the girl walks at a steady speed of 1 m s-1, calculate the time
she takes to get from × to Z.
Calculate her resultant velocity.
40 m
30 m
16.
Find the resultant force in the following cases:
17.
An aircraft has a maximum speed of 1000 km h-1.
If it is flying north into a headwind speed 100 km h-1 what is the maximum velocity of
the aircraft?
18.
A model aircraft is flying north with a velocity of 24 m s-1.
A wind is blowing from west to east at 10 m s-1.
What is the resultant velocity of the plane?
19.
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?
20.
State what is meant by a vector quantity and scalar quantity.
Give two examples of each.
21.
Find the average speed and average velocity of the following.
An orienteer who runs 5 km due South, 4 km due West and then 2 km North in 1
hour.
22.
A ship is sailing East at 4 m s-1. A passenger walks due North at 2 m s-1.
What is the resultant velocity of the passenger relative to the sea?
Answers
(Use both scale drawing and trigonometry).
23.
A man pulls a garden roller with a maximum force of 50 N.
Find his effective horizontal force.
Without changing the force applied, explain how he could increase this effective
force.
24.
A barge is dragged along a canal as shown below.
barge
What is the component of the force parallel to the canal?
25.
A toy train of mass 0.2 kg, is given a push of 10 N at an angle of 300 to the rails.
Calculate a) the component of force along the rails
b) the acceleration of the train.
26.
A football is kicked up at an angle of 700 at 15 m s-1.
Calculate a) the horizontal component of the velocity
b) the vertical component of the velocity?
Answers
Equations of Motion
27.
The graph below shows how the acceleration of an object varies with time.
The object started from rest.
a / m s-2
4
2
0
10
5
t/s
Draw a velocity time graph for the first 10 s of the motion.
28.
The velocity time graph
for an object is shown below.
v / m s-1
Velocity
(m s - 1)
t/s
10
5
0
2
3
10
4
3
Draw the corresponding acceleration-time graph.
(Put numerical valuesv on
/ mtime
s-1 axis).
29.
The graph shows the velocity of a ball which is dropped and bounces from a floor.
A downwards direction is taken as being positive.
B
t/s
+
E
0
-
D
C
During section OB of the graph
in which direction is the ball travelling?
what can you say about the speed of the ball?
During section CD of the graph
in which direction is the ball travelling?
what can you say about the speed of the ball?
During section DE of the graph
in which direction is the ball travelling?
what can you say about the speed of the ball?
What happened to the ball at point B on the graph?
What happened to the ball at point C on the graph?
What happened to the ball at point D on the graph?
How does the speed of the ball immediately after rebound compare with the speed
immediately before?
Answers
30.
Which velocity-time graph below represents the motion of a ball which is thrown
vertically upwards and returns to the thrower 3 seconds later?
31.
A ball is dropped from a height and bounces up and down on a horizontal surface.
Assuming that there is no loss of kinetic energy at each bounce, select the
velocity-time graph which represents the motion of the ball from the moment it is
released.
v / m s-1 -1
v/ms
v / m s-1 -1
v/ms
v / m s-1 -1
v/ms
t/s
t/s
A
A
B
B
v / m s-1 -1
v/ms
0
t/s
t/s
C
C
v / m s-1 -1
v/ms
0
D
D
32.
t/s
t/s
t/s
t/s
E
E
t/s
t/s
A ball is dropped from rest and bounces several times, losing some kinetic energy at
each bounce. Selected the correct velocity - time graph for this motion.
v / m s-1
v / m s-1
v / m s-1
t/s
t/s
A
t/s
B
v / m s-1
C
v / m s-1
t/s
t/s
D
E
Answers
33.
An object accelerates uniformly at 4 m s-2 from an initial speed of 8 m s-1. How far
does it travel in 10 s?
34.
A car accelerates uniformly at 6 m s-2, its initial speed is 15 m s-1 and it covers a
distance of 200 m. Calculate its final velocity.
35.
A ball is thrown to a height of 40 m above its starting point, with what velocity was it
thrown?
36.
A car travelling at 30 m s-1 slows down at 1.8 m s-2 over a distance of 250 m. How
long does it take to stop?
37.
If a stone is thrown vertically down a well at 5 m s-1. Calculate the time taken for the
stone to reach the water surface 60 m below.
38.
A tennis ball launcher is 0.6 m long and the velocity of a tennis ball leaving the
launcher is 30 m s-1.
Calculate: a) the average acceleration of a tennis ball
b) the time of transit in the launcher.
39.
In an experiment to find “g” a steel ball falls from rest through 40 cm. The time taken
is 0.29 s. What is the value for “g”.
40.
A trolley accelerates down a slope. Two photo-cells spaced 0.5 m apart measure the
velocities to be 20 cm s-1 and 50 cm s-1.
Calculate a) the acceleration of the trolley
b) the time taken to cover the 0.5 m.
41.
A helicopter is rising vertically at 10 m s-1 when a wheel falls off.
The wheel hits the ground 8 s later. Calculate at what height the helicopter was flying
when the wheel came off.
42.
A ball is thrown upwards from the side of a cliff as shown below.
a) Calculate:
i) the height of the ball above sea level after 2 s
ii) the ball’s velocity after 2 s.
b) What is the total distance travelled by the ball from launch to landing in the sea?
Answers
43.
A box is released from a plane travelling with a horizontal velocity of 300 m s-1 and a
height of 300 m, find:
a) how long it takes the box to hit the ground
b) the horizontal distance between the point of impact and the release point
c) the position of the plane relative to the box at the time of impact.
44.
A projectile is fired horizontally from the edge of a cliff at 12 m s-1 and hits the sea
60 m away. Find:
a) the time of flight
b) the height of the starting point above sea level.
State any assumptions you have made.
45.
A ball is projected horizontally at 15 m s-1 from the top of a vertical cliff. It reaches
the horizontal ground 45 m from the foot of the cliff.
a) Draw graphs, giving appropriate numerical values of the ball’s
i) horizontal speed against time
ii) vertical speed against time, for the period between projection until it hits the
ground
b) Use a vector diagram, to find the velocity of the ball 2 s after its projection.
(Magnitude and direction are required).
46.
A projectile is fired across level ground taking 6 s to travel from A to B.
The highest point reached is C. Air resistance is negligible.
vH/m s-1
vv/m s-1
t/s
t/s
a) Describe:
i) the horizontal motion of the projectile
ii) the vertical motion of the projectile?
b) Use a vector diagram, to find the speed and angle at which the projectile was fired
from point A.
c) Find the speed at position C. Explain why this is the smallest speed of the
projectile.
d) Calculate the height above the ground of point C.
e) Find the range AB.
Answers
47.
An object of mass 5 kg is propelled with a speed of 40 m s-1 at an angle of 30o to the
horizontal.
Find:
a) the vertical component of its initial velocity
b) the maximum vertical height reached
c) the time of flight for the whole trajectory
d) the horizontal range of the object.
48.
A missile is launched at 60° to the ground and strikes a target on a hill as shown
below.
If the initial speed of the missile was 100 m s-1 find:
a) the time taken to reach the target
b) the height of the target above the launcher.
49.
A stunt driver hopes to jump across a canal of width 10 m.
The drop to the other side is 2 m as shown.
a) Calculate the horizontal speed required to make it to the other side
b) State any assumptions you have made.
50.
Describe how you could measure the acceleration of trolley starting from rest moving
down a slope. You are provided with a metre stick and stop clock. Your description
should include:
a) a diagram
b) a list of measurements taken
c) how you would use these measurements to calculate the acceleration.
d) how you would estimate the uncertainties involved in the experiment.
Answers
Newton’s 2nd Law, energy and power
51.
State Newton’s 1st Law of Motion.
52.
A lift of mass 500 kg travels upwards at a constant speed.
Calculate the tension in the lifting table.
53.
(a) A fully loaded oil tanker has a mass of 2.0 × 108 kg.
As the speed of the tanker increases from zero to a steady maximum speed of
8.0 m s-1 the force from the propellers remains constant at 3.0 × 106 N.
(i)
(ii)
Calculate the acceleration of the tanker just as it starts from rest.
What is the size of the force of friction acting on the tanker when it is
travelling at the steady speed of 8.0 m s-1?
(b) When its engines are stopped, the tanker takes 50 minutes to come to rest from a
speed of 8.0 m s-1. Calculate its average deceleration.
54.
v / m s-1
B
A
C
0
D
E t/s
The graph shows how the speed of a parachutist varies with time after having jumped
from the aeroplane. With reference to the letters, explain each stage of the journey.
55.
Two girls push a car of mass 2000 kg. Each applies a force of 50 N and the force of
friction is 60 N. Calculate the acceleration of the car.
56.
A boy on a skateboard rides up a slope. The total mass of the boy and the skateboard
is 90 kg. He decelerates uniformly from 12 m s-1 to 2 m s-1 in 6 seconds. Calculate the
resultant force acting on him.
57.
A box is pulled along a rough surface with a constant force of 140 N. If the mass of
the box is 30 kg and it accelerates at 4 m s-2 calculate:
(a) the unbalanced force causing the acceleration
(b) the force of friction between the box and the surface.
Answers
58.
An 800 kg Metro is accelerated from 0 to 18 m s-1 in 12 seconds.
(a) What is the resultant force acting on the Metro?
(b) How far does the car travel in these 12 seconds?
At the end of the 12 s period the brakes are operated and the car comes to rest in a
distance of 50 m.
(c) What is the average frictional force acting on the car?
59.
(a) A rocket of mass 40000 kg is launched vertically upwards. Its engines produce a
constant thrust of 700000 N.
(i) Draw a diagram showing all the forces acting on the rocket.
(ii) Calculate the initial acceleration of the rocket.
(b) As the rocket rises its acceleration is found to increase. Give three reasons for
this.
(c) Calculate the acceleration of the same rocket from the surface of the Moon if the
Moon’s gravitational field strength is 1.6 N kg-1.
(d) Explain in terms of Newton’s laws of motion why a rocket can travel from the
Earth to the Moon and for most of the journey not burn up any fuel.
60.
A rocket takes off and accelerates to 90 m s-1 in 4 s. The resultant force acting on it is
40 kN upwards.
(a) Calculate the mass of the rocket.
(b) Calculate the force produced by the rocket’s engines if the average force of
friction is 5000 N.
61.
What is the minimum force required to lift a helicopter of mass 2000 kg upwards with
an initial acceleration of 4 m s-2. Air resistance is 1000 N.
62.
A crate of mass 200 kg is placed on a balance in a lift.
(a) What would be the reading on the balance, in newtons, when the lift was
stationary?
(b) The lift now accelerates upwards at 1.5 m s-2. What is the new reading on the
balance?
(c) The lift then travels up at a constant speed of 5 m s-1. What is the reading on the
balance?
(d) For the last stage of the journey calculate the reading on the balance when the lift
decelerates at 1.5 m s-2 while moving up.
63.
A small lift in a hotel is fully loaded and has a mass of 250 kg. For safety reasons the
tension in the pulling cable must never be greater than 3500 N.
(a) What is the tension in the cable when the lift is:
(i) at rest
(ii) moving up at a constant 1 m s-1
(iii) accelerating upwards at 2 m s-2
(iv) accelerating downwards at 2 m s-2?
(b) Calculate the maximum permitted upward acceleration of the fully loaded lift.
(c) Describe a situation where the lift could have an upward acceleration greater than
the value in (b) without breaching safety regulations.
Answers
64.
A package of mass 4 kg is hung from a spring balance attached to the ceiling of a lift
which is accelerating upwards at 3 m s-2. What is the reading on the spring balance?
65.
The graph shows how the downward speed of a lift varies with time.
v / m s-1
0
4
10
12
t/s
(a) Draw the corresponding acceleration/time graph.
(b) A 4 kg mass is suspended from a spring balance inside the lift. Determine the
reading on the balance at each stage of the motion.
66.
Two masses are pulled along a flat surface as shown below.
Find the (a) acceleration of the masses
(b) tension, T.
67.
A car of mass 1200 kg tows a caravan of mass 1000 kg. The frictional force on the
car and caravan is 200 N and 500 N respectively. The car accelerates at 2 m s-2.
(a) Calculate the force exerted by the engine of the car.
(b) What force does the tow bar exert on the caravan?
(c) The car then travels at a constant speed of 10 m s-1.
Assuming the frictional forces to be unchanged calculate the new engine force
and the force exerted by the tow bar on the caravan.
(d) The car brakes and decelerates at 5 m s-2.
Calculate the force exerted by the brakes (assume the other frictional forces
remain constant).
Answers
68.
A tractor of mass 1200 kg pulls a log of mass 400 kg. The tension in the tow rope is
2000 N and the frictional force on the log is 800 N. How far will the log move in 4 s
assuming it was stationary to begin with?
69.
A force of 60 N pushes three blocks as shown.
If each block has a mass of 8 kg and the force of friction on each block is 4 N
calculate:
(a) the acceleration of the blocks
(b) the force block A exerts on block B
(c) the force block B exerts on block C.
The pushing force is then reduced until the blocks move at constant speed.
(d) Calculate the value of this pushing force.
(e) Does the force block A exerts on block B now equal the force block B exerts on
block C? Explain.
70.
A 2 kg trolley is connected by string to a 1 kg mass as shown. The bench and pulley
are frictionless.
(a) Calculate the acceleration of the trolley.
(b) Calculate the tension in the string.
71.
A force of 800 N is applied to a canal barge by means of a rope angled at 40° to the
direction of the canal. If the mass of the barge is 1000 kg and the force of friction
between the barge and the water is 100 N find the acceleration of the barge.
72.
A crate of mass 100 kg is pulled along a rough surface by two ropes at the angles
shown.
(a) If the crate is moving at a constant speed of 1 m s-1 what is the force of friction?
(b) If the forces were increased to 140 N at the same angle calculate the acceleration
of the crate.
Answers
73.
A 2 kg block of wood is placed on the slope shown. It remains stationary. What is
the size of the frictional force acting up the slope?
74.
A 500 g trolley runs down a runway which is 2 m long and raised 30 cm at one end.
If
its speed remains constant throughout calculate the force of friction acting up the
slope.
75.
The brakes on a car fail while it is parked at the top of a hill. It runs down the hill for
a distance of 50 m until it crashes into a hedge. The mass of the car is 900 kg and the
hill makes an angle of 15° to the horizontal. If the average force of friction is 300 N
find:
(a) the component of weight acting down the slope
(b) the acceleration of the car
(c) the speed of the car as it hits the hedge
(d) the force acting perpendicular to the car (the reaction) when it is on the hill.
Momentum and impulse
76.
What is the momentum of the object in each of the following situations :
(a)
(b)
(c)
77.
A trolley of mass 2 kg and travelling at 1.5 m s-1 collides and sticks to another
stationary trolley of mass 2 kg. Calculate the velocity after the collision. Show that
the collision is inelastic.
78.
A target of mass 4 kg hangs from a tree by a long string. An arrow of mass 100 g is
fired with a velocity of 100 m s-1 and embeds itself in the target. At what velocity
does the target begin to move after the impact?
Answers
79.
A trolley of mass 2 kg is moving at constant speed when it collides and sticks to a
second trolley which was originally stationary. The graph shows how the speed of the
2 kg trolley varies with time.
v / m s-1
0.5
0.2
0
t/s
Determine the mass of the second trolley.
80.
In a game of bowls one particular bowl hits the jack ‘straight on’ causing it to move
forward. The jack has a mass of 300 g and was originally stationary, the bowl has a
mass of 1 kg and was moving at a speed of 2 m s-1.
(a) What is the speed of the jack after the collision if the bowl continued to move
forward at 1.2 m s-1?
(b) How much kinetic energy is lost during the collision?
81.
In space two spaceships make a docking manoeuvre (joining together). One spaceship
has a mass of 1500 kg and is moving at 8 m s-1. The second spaceship has a mass of
2000 kg and is approaching from behind at 9 m s-1. Determine their common velocity
after docking.
82.
Two cars are travelling along a racing track. The car in front has a mass of 1400 kg
and is moving at 20 m s-1 while the car behind has a mass of 1000 kg and is moving at
30 m s-1. They collide and the car in front moves off with a speed of 25 m s-1.
(a) Determine the speed of the rear car after the collision.
(b) Show clearly whether this collision was elastic or inelastic.
83.
One vehicle approaches another from behind as shown. The vehicle at the rear is
moving faster than the one in front and they collide which causes the vehicle in front
to be ‘nudged’ forward with an increased speed. Determine the speed of the rear
vehicle after the collision.
84.
A trolley of mass 0.8 kg, travelling at 1.5 m s-1 collides head on with another vehicle
of mass 1.2 kg, travelling at 2.0 m s-1 in the opposite direction. They lock together on
impact. Determine the speed and direction after the collision.
Answers
85.
A firework is launched vertically and when it reaches its maximum height it explodes
into 2 pieces. One piece has a mass of 200 g and moves off with a speed of 10 m s-1.
If the other piece has a mass of 120 g what speed does it have?
86.
Two trolleys in contact, initially at rest, fly apart when a plunger is released. One
trolley with a mass of 2 kg moves off with a speed of 4 m s-1 and the other with a
speed, in the opposite direction, of 2 m s-1. What is the mass of this trolley?
87.
A man of mass 80 kg and woman of mass 50 kg are skating on ice. At one point they
stand next to each other and the woman pushes the man who then moves away at
0.5 m s-1. With what speed and at what direction does the woman move off?
88.
Two trolleys in contact, initially at rest, fly apart when a plunger is released. If one
has a mass of 2 kg and moves off at speed of 2 m s-1, calculate the velocity of the
other trolley given its mass is 3 kg.
89.
A cue exerts an average force of 7 N on a stationary snooker ball of mass 200 g. If
the impact lasts for 45 ms, with what speed does the ball leave the cue?
90.
A girl kicks a football of mass 500 g which was originally stationary. Her foot is in
contact with the ball for a time of 50 ms and the ball moves off with a speed of
10 m s-1. Calculate the average force exerted on the ball by her foot.
91.
A stationary golf ball is struck by a club. The ball which has a mass of 100 g moves
off with a speed of 30 m s-1. If the average force of contact is 100 N calculate the
time of contact.
92.
The graph shows how the force exerted on a hockey ball by a hockey stick varies with
time. If the mass of the ball is 150 g determine the speed of the ball as it leaves the
stick (assume that it was stationary to begin with).
F/N
40 N
20
93.
t / ms
A ball of mass 100 g falls from a height of 20 cm onto a surface and rebounds to a
height of 18 cm. The duration of impact is 25 ms. Calculate:
(a) the change in momentum of the ball caused by the ‘bounce’
(b) the average force exerted on the ball by the surface.
Answers
94.
A rubber ball of mass 40 g is dropped from a height of 0.8 m onto the pavement.
It rebounds to a maximum height of 0.45 m. The average force of contact between
the pavement and the ball is 2.8 N.
(a) Calculate the velocity of the ball just before it hits the ground and the velocity
just after hitting the ground.
(b) Calculate the time of contact between the ball and pavement.
95.
A ball of mass 400 g travels horizontally along the ground and collides with a wall.
The velocity / time graph below represents the motion of the ball for the first 1.2
seconds.
v / m s-1
A
-4
(a)
(b)
(c)
(d)
B
6
C
0.6
0.8
1.2
E
t/s
D
Describe the motion of the ball during sections AB, BC, CD and DE.
What is the time of contact with the wall?
Calculate the average force between the ball and the wall.
How much energy is lost due to contact with the wall?
96.
Water is ejected from a fire hose at a rate of 25 kg s-1 and a speed of 50 m s-1. If the
water hits a wall calculate the average force exerted on the wall. Assume that the
water does not rebound from the wall.
97.
A rocket burns fuel at a rate of 50 kg per second, ejecting it with a constant speed of
1800 m s-1. Calculate the force exerted on the rocket.
98.
Describe in detail an experiment which you would do to determine the average force
between a football boot and a football as it is being kicked. Draw a diagram of the
apparatus and include all measurements taken and calculations carried out.
99.
A 2 kg trolley travelling at 6 m s-1 collides with a stationary 1 kg trolley.
(a) If they remain connected, calculate:
(i) their combined velocity
(ii) the momentum gained by the 1 kg trolley
(iii) the momentum lost by the 2 kg trolley.
(b) If the collision time is 0.5 s, find the force acting on each trolley.
Answers
Density and pressure
1.
A block of iron has a mass of 40000 kg and a volume of 5 m3. What is its density?
2.
What is the mass of a cylinder of aluminium with a volume of 2.5 m3?
(The density of aluminium is 2700 kg m-3 )
3.
1 kg of nitrogen gas is used to fill a balloon. If the density of nitrogen is 1.25 kg m-3,
find the volume of the balloon.
4.
A tank measures 60 cm long and 40 cm wide. 72 kg of water are to be poured into the
tank. How deep will the water be? (Density of water is 1000 kg m-3)
5.
What will be the mass of air in a classroom with the dimensions: length 15 m, breadth
10 m and height 4 m? (The density of air is 1.3 kg m-3).
6.
In the diagram below the piston contains 0.2 kg of oxygen, which has a density of
1.43 kg m-3.
(a) If the plunger is at height of 40 cm, what is the cross-sectional area of the
plunger?
(b) The gas is heated and the plunger rises a further 20 cm.
What is the density of the oxygen now?
7.
0.01 m3 of water is heated until it all changes to steam. What will be the approximate
volume of the steam?
8.
Solids and liquids are approximately 1000 times denser than gases. How will the
separation of the particles compare in each case?
9.
Describe an experiment to measure the density of air. Your answer should include:
(a) a diagram of the apparatus used
(b) a list of measurements taken
(c) any necessary calculations.
Answers
10.
Explain why the use of large tyres helps to prevent a tractor from sinking into soft
ground.
11.
A box weighs 120 N and has a base area of 2 m2. What pressure does it exert on the
ground?
12.
If atmospheric pressure is 100000 Pa, what force does the air exert on a wall of area
10 m2 ?
13.
A rectangular steel block measures 10 cm × 8 cm × 6 cm.
What is the greatest and the least pressure which it can exert on a surface?
(Density of steel is 8000 kg m-3)
14.
Estimate the pressure you exert on the floor when you are standing on one foot.
15.
What is the pressure due to a depth of 10 m of water?
(Density of water = 1000 kg m-3).
16.
A water tank has a base of cross-sectional area 0.5 m2 and a depth of water 1.5 m.
Calculate:
(a) the pressure at the bottom of the tank (caused by the water and by the pressure of
the air above the water )
(b) the resultant force on the base.
17.
Water is supplied to flats from a tank on the roof. Find the extra water pressure
available to residents on the ground floor if their taps are 30 m below the level of the
taps on the top floor.
18.
A cube of side 12 cm is completely immersed in a liquid of density 800 kg m-3, so that
the top surface is horizontal and 20 cm below the surface of the liquid.
Calculate the fluid pressure:
(a) at a depth of 20 cm
(b) at a depth of 32 cm.
(c) Hence calculate the force exerted on:
i) the top surface of the cube
ii) the bottom surface of the cube.
(d) Calculate the size and direction of the vertical force due to this pressure
difference.
Answers
19.
A cube of wood of sides 0.5 m floats in a large tank of water at a height of 0.3 m
above the surface.
Calculate the:
(a) weight of the cube
(b) vertical upthrust given to the cube by the water
(c) volume of water displaced by the cube.
(density of water = 1000 kg m-3 ; density of wood = 400 kg m-3)
20.
Explain why it is very easy to float in the Dead Sea.
Gas laws
Pressure and volume (constant temperature)
21.
100 cm3 of air is contained in a syringe at atmospheric pressure ( 105 Pa ).
If the volume is reduced to a) 50 cm3 or b) 20 cm3 without a change in
temperature, what will be the new pressures ?
22.
If the piston in a cylinder containing 300 cm3 of gas at a pressure of 105 Pa is moved
outwards so that the pressure of the gas falls to 8 × 104 Pa, find the new volume of
the gas.
23.
A weather balloon contains 80 m3 of helium at normal atmospheric pressure of 105 Pa.
What will be the volume of the balloon at an altitude where air pressure is 8 × 104 Pa?
24.
The cork in a pop-gun is fired when the pressure reaches 3 atmospheres. If the
plunger is 60 cm from the cork when the air in the barrel is at atmospheric pressure,
how far will the plunger have to move before the cork pops out?
Answers
25.
A swimmer underwater uses a cylinder of compressed air which holds 15 litres of air
at a pressure of 12000 kPa.
(a) Calculate the volume this air would occupy at a depth where the pressure is
200 kPa.
(b) If the swimmer breathes 25 litres of air each minute at this pressure, calculate
how long the swimmer could remain at this depth (assume all the air from the
cylinder is available).
Pressure and temperature (constant volume)
26.
Convert the following celsius temperatures to kelvin.
a) -273 °C
b) -150 °C
c) 0 °C d) 27 °C
e) 150 °C
27.
Convert the following kelvin temperatures to celsius.
a) 10 K b) 23 K
c) 100 K
d) 350 K
e) 373 K
28.
A cylinder of oxygen at 27 °C has a pressure of 3 × 106 Pa. What will be the new
pressure if the gas is cooled to 0 °C?
29.
An electric light bulb is designed so that the pressure of the inert gas inside it is
100 kPa (normal air pressure) when the temperature of the bulb is 350 °C. At what
pressure must the bulb be filled if this is done at 15 °C ?
30.
The pressure in a car tyre is 2.5 × 105 Pa at 27 °C. After a long journey the pressure
has risen to 3.0 × 105 Pa. Assuming the volume has not changed, what is the new
temperature of the tyre?
31.
A compressed air tank which at room temperature of 27 °C normally contains air at 4
atmospheres, is fitted with a safety valve which operates at 10 atmospheres.
During a fire the safety valve was released. Estimate the average temperature of the
air in the tank when this happened.
32.
(a) Describe an experiment to find the relationship between the pressure and
temperature of a fixed mass of gas at constant volume. Your answer should
include:
(i) a labelled diagram of the apparatus
(ii) a description of how you would use the apparatus
(iii) the measurements you would take.
(b) Use the following results to plot a graph of pressure against temperature in °C
using axes as shown below.
Pressure / kPa
91
98
104 110 117
Temperature / ° C
0
20
40
60
p / kPa
80
-300
0
100 T / ° C
Answers
(i) Explain why the graph you have drawn shows that pressure does not vary
directly as celsius temperature.
(ii) Explain how the graph can be used to show direct variation between
temperature and pressure if a new temperature scale is introduced.
(iii) Use the graph to estimate the value in °C of the zero on this new temperature
scale.
(c) Use the particle model of a gas to explain the following:
(i) why the pressure of a fixed volume of gas decreases as its temperature
decreases
(ii) why the pressure of a gas at a fixed temperature decreases if its volume
increases
(iii) what happens to the molecules of a gas when Absolute Zero is reached.
Volume and temperature (constant pressure)
33.
Describe an experiment to find the relationship between the volume and temperature
of a fixed mass of gas at constant pressure. Your description should include:
(a) a diagram of the apparatus used
(b) a note of the results taken
(c) an appropriate method to find the relationship using the results.
34.
100 cm3 of a fixed mass of air is at a temperature of 0 °C. At what temperature will
the volume be 110 cm3 if its pressure remains constant.
35.
Air is trapped in a glass capillary tube by a bead of mercury. The volume of air is
found to be 0.10 cm3 at a temperature of 27 °C. Calculate the volume of air at a
temperature of 87 °C.
36.
The volume of a fixed mass of gas at constant temperature is found to be 50 cm3.
The pressure remains constant and the temperature doubles from 20 °C to 40 °C.
Explain why the new volume of gas is not 100 cm3.
General gas equation
37.
Given, for a fixed mass of gas, p  T and p  1/V, derive the general gas equation.
38.
Find the unknown quantity from the readings shown below for a fixed mass of gas.
(a) p1 = 2 × 105 Pa
V1 = 50 cm3
T1 = 20 °C
5
p2 = 3 × 10 Pa
V2 = ?
T2 = 80 °C
(b) p1 = 1 × 105 Pa
V1 = 75 cm3
T1 = 20 °C
5
3
p2 = 2.5 × 10 Pa
V2 = 100 cm
T2 = ?
(c) p1 = 2 × 105 Pa
V1 = 60 cm3
T1 = 20 °C
3
p2 = ?
V2 = 80 cm
T2 = 150 °C
d)
p1 = 1 × 105 Pa
V1 = 75 cm3
T1 = ?
p2 = 2.5 × 105 Pa
V2 = 50 cm3
T2 = 40 °C
Answers
39.
A sealed syringe contains 100 cm3 of air at atmospheric pressure 105 Pa and a
temperature of 27 °C. When the piston is depressed the volume of air is reduced to 20
cm3 and this produces a temperature rise of 4 °C. Calculate the new pressure of the
gas.
40.
Calculate the effect the following changes have on the pressure of a fixed mass of gas.
(a) Its temperature (in K) doubles and volume halves.
(b) Its temperature (in K) halves and volume halves.
(c) Its temperature (in K) trebles and volume quarters.
41.
Calculate the effect the following changes have on the volume of a fixed mass of gas.
(a) Its temperature (in K) doubles and pressure halves.
(b) Its temperature (in K) halves and pressure halves.
(c) Its temperature (in K) trebles and pressure quarters.
42.
Explain the pressure-volume, pressure-temperature and volume-temperature laws
qualitatively in terms of the kinetic model.
Answers
NUMERICAL ANSWERS
Revision
1.
–
2.
6.8 m s-1
3.
1.44 × 1011 m
4.
181 minutes
5.
a) 5 m s-1 b) 35 m c) 10 m s-1 d) 100 m e) 135 m
6.
750 m s-1
7.
5s
8.
2s
9.
0.1 s
10.
a) 2 m s-2 b) 6 s
11.
a) 5 m s-2 b) 50 m s-1 c) 7 s
12.
0.2 m s-2
13.
(5.20 + 0.01) m s-2
Vectors
14.
a) 80 km b) 40 km h-1 c) 20 km h-1 (000) d) 10 km h-1 (000).
15.
a) 70 m b) 50 m (037) c) 70 s d) 0.71 m s-1 (037)
16.
a) 6.8 N (077) b) 11.3 N (045) c) 6.4 N (129)
17.
900 km h-1 (000)
18.
26 m s-1 (023)
19.
804 km h-1 (354)
20.
21.
a) 11 km h-1 b) 5 km h-1 (233)
22.
4.5 m s-1 (063)
23.
24.
353.6 N
25.
43.5 m s-2
26.
vx = 5.1 m s-1 vy = 14.1 m s-1
Equations of motion
30.
D
31.
A
32.
A
33.
280 m
34.
51.2 m s-1
35.
28 m s-1
36.
16.7 s
37.
3.1 s
38.
750 m s-2
39.
9.5 N kg-1
40.
0.21 m s-2
41.
234 m
42.
a) i) 21.4 m ii) 15.6 m s-1 b) 34.6 m
43.
a) 7.8 s b) 2340 m
44.
a) 5 s b) 122.5 m
45.
a) b) 33 m s-1 (153)
46.
a) b) 50 m s-1 (053) c) 40 m s-1 d) 45 m e) 240 m
47.
a) 20 m s-1 b) 20.4 m c) 141.9 m
Answers
48.
49.
50.
a) 8 s b) 379 m
a) 15.6 m s-1
-
Newton’s 2nd Law, energy and power
51.
52.
4900 N
53.
a) i) 0.015m s-2 ii) 3.0 × 106 N b) - 0.0027 m s-2
54.
55.
0.02 m s-2
56.
150 N
57.
a) 120 N b) 20 N
58.
a) 1200 N b) 108 m c) 2592 N
59.
a) i) ii) 7.7 m s-2 b) c) 15.9 m s-2 d) 60.
a) 1778 kg b) 62424 N
61.
28600 N
62.
a) 1960 N b) 2260 N c) 1960 N d) 1660 N
63.
a) i) 2450 N ii) 2450 N iii) 2950 N iv) 1950 N b) 4.2 m s-2 c) 64.
51.2 N
65.
a) b) 37.2 N, 39.2 N, 43.2 N
66.
a) 8 m s-2 b) 16 N
67.
a) 5100 N b) 2500 N c) 700 N, 500 N d) 10,300 N
68.
24 m
69.
a) 2 m s-2 b) 40 N c) 20 N d) 12 N e)
70.
a) 3.27 m s-2 b) 6.54 N
71.
0.513 ms-2
72.
a) 225.5 N b) 0.376 m s-2
73.
9.8 N
74.
0.735 N
75.
a) 2283 N b) 2.2 m s-2 c) 14.8 m s-1 d) 8520 N
Momentum and impulse
76.
a) 20 kg m s-1 to the right b) 500 kg m s-1 downwards c) 9 kg m s-1 to the left
77.
0.75 m s-1
78.
2.4 m s-1
79.
3 kg
80.
a) 2.7 m s-1 b) 0.19 J
81.
8.6 m s-1
82.
a) 23 m s-1
83.
8.67 m s-1
84.
0.6 m s-1 as initial direction of second vehicle
85.
16.7 m s-1
86.
4 kg
87.
0.8 m s-1 in opposite direction
88.
1.3 m s-1
89.
1.58 m s-1
90.
100 N
91.
0.03 s
92.
2.67 m s-1
93.
94.
a) -0.39 kg m s-1 b) 15.6 N
a) 4 m s-1, 3 m s-1 b) 0.1 s
Answers
95.
96.
97.
98.
99.
b) 0.2 s c) 20 N d) 4.0 J
1250 N
9 × 104 N
a) i) 4 m s-1 ii) 4 kg m s-1 iii) 4 kg m s-1 b) 8 N
Density and pressure
1.
8000 kg m-3
2.
m = 6750 kg
3.
0.8 m3
4.
depth = 0.3 m
5.
m = 780 kg
6.
a) 0.35 m2 b) 0.95 kg m-3
7.
approx. 10 m3
8.
9.
10.
11.
60 Pa
12.
106 N
13.
Max. = 8 x103 Pa Min. = 4.8 x103 Pa
14.
15.
9.8 × 104 Pa
16.
a) 2.48 x104 Pa b) 1.24 x104 N
17.
3 x105 Pa
18.
a) 1600 Pa b) 2560 Pa c) i)23.04 N ii) 36.86 N d) 13.82 N
19.
i) 500 N ii) 500 N iii) 0.05 m3 iv) 500 N
20.
Gas laws
22.
a) 2 x105 Pa b) 5 x105 Pa
22.
375 cm3
23.
100 m3
24.
40 cm
25.
a) 900 litres b) 36 minutes
26.
27.
28.
2.73 x106 Pa
29.
p = 4.6 x104 Pa
30.
T = 87 °C
31.
T = 477 °C
32.
33.
34.
300 K
35.
0.012 cm3
36.
37.
38.
a) 40 cm3 b) 977 K c) 2.2 × 105 Pa d) 188 K
39.
5.1 × 105 Pa
40.
41.
42.
-