Grade 11
28 FEBRUARY 2011
PHYSICS :
REVISION
NEWTONIAN MECHANICS
QUESTION 1
There are four possible options for each answer in the following questions. Each question has
only ONE correct answer. Choose the correct answer and write only A, B, C or D next to the
question number.
1.1
A book rests on a horizontal table, as shown in the following diagram. The force, W,
represents the weight of the book.
According to Newton’s third law of motion, the force that is paired with the weight is …
1.2
A
the force that the table exerts upwards on the book
B
the force that the book exerts on the Earth
C
the force that the book exerts on the table
D
the force that the Earth exerts on the book
(3)
A force, F, acts on a body of mass, m, and produces an acceleration, a. If you double
mass of the body while the force remains constant, the acceleration will …
A
increase to 4a
B
decrease to
1
a
4
C
decrease to
1
a
2
D
increase to 2a
(3)
1.3
1.4
1.5
1.6
An object has a mass m on the surface of the Earth. A rocket transports the object to a
planet that has a mass 8 times that of the Earth and a radius twice that of the Earth.
Which of the following is the mass of the object on the planet?
A
8m
B
4m
C
2m
D
m
(3)
You apply a constant resultant force to a body that can move freely. Which of the
following quantities remains constant?
A
the body’s acceleration
B
the body’s velocity
C
the body’s speed
D
the body’s momentum
(3)
Two forces of magnitudes 8 N and 6 N are added to each other. Which of the following
values CANNOT be a resultant of these two forces?
A
2N
B
3N
C
14 N
D
16 N
(3)
You can replace two forces, P and Q, with a single force of 7 N. If the magnitude of
force P is 3 N, which one of the following can be the magnitude of force Q?
A
2N
B
3N
C
8N
D
13 N
(3)
2
1.7
The man in the following diagram is holding a 400 N load. The man’s weight is 900 N.
What is the reaction force on his shoes due to the floor?
1.8
A
1 300 N
B
900 N
C
500 N
D
400 N
(3)
Your weight acts vertically downwards.
Which one of the following forces balances your weight so that you do not fall through
the floor?
A
the force of gravity on the Earth from your body
B
the force of gravity on your body from the Moon
C
the reaction force on the floor from your feet
D
the reaction force on your feet from the floor
3
(3)
1.9
The following diagram shows a head-on collision that is about to take place between
two vehicles. The truck has a mass of 25 000 kg and travels at 25 ms–1 towards a car
of mass 800 kg travelling at 30 ms–1 towards the truck.
Calculate the magnitude of the total momentum.
1.10
A
649 000 kgms–1
B
624 000 kgms–1
C
625 000 kgms–1
D
601 000 kgms–1
(3)
A model toy car is at rest. The owner moves the car from its rest position along a
straight horizontal track. He uses a motor that exerts a constant driving force. You can
ignore the effects of friction and air resistance.
Which graph best represents the momentum of the car versus time?
A
B
C
D
(3)
[30]
4
QUESTION 2
Indicate whether the following statements are TRUE or FALSE. Write only ‘True’ or ‘False’ next
to the question number. If the statement is FALSE, write down the correct statement.
2.1
The inertia that an object has depends on the resultant force that acts on it.
(2)
2.2
The gravitational constant, G, will be different if you measure it on another planet.
(2)
2.3
If an object moves with a constant velocity, then no forces are acting on the object.
(2)
2.4
We define gravitational field strength as the potential energy per unit mass.
(2)
2.5
You can use a free-body diagram to analyse a given problem only if the forces that act
on the body are all contact forces.
(2)
For a given surface, the coefficient of kinetic friction, k, is smaller than the coefficient of
static friction.
(2)
Each team in a tug-of-war competition exerts a force of 800 N on a rope. Therefore, the
tension in the rope is 1 600 N.
(2)
Momentum is a vector quantity.
(2)
2.6
2.7
2.8
[16]
QUESTION 3
Give one word or term for each of the following descriptions. Write only the word or term next to
the question number.
3.1
The property an object has that causes it to resist a change in its state of rest or motion
(1)
3.2
A resultant force that acts on an object causes the object to undergo …
(1)
3.3
The force experienced by an object on or near the surface of the Earth
(1)
3.4
A perpendicular force exerted by a surface on an object in contact with the surface
(1)
3.5
The single force that produces the same effect on an object as a number of forces that
act together
(1)
3.6
The state of an object where there is no change in its motion
(1)
3.7
The product of a net force and the time interval over which the net force acts
(1)
3.8
The relationship between impulse and change of momentum
(1)
[8]
5
QUESTION 4
You pull a block along a rough horizontal table with a force of 14 N and a constant velocity.
When you increase the pulling force to 31 N, the block accelerates at 8,5 ms–2.
Calculate the following.
4.1
the frictional force between the block and the table
(2)
4.2
the mass of the block
(4)
4.3
the coefficient of kinetic friction, k, between the block and the table
(4)
[10]
QUESTION 5
The following diagram shows a block with mass 150 kg hanging from a crane on a cable. The
crane winds up the cable so that the block accelerates upwards at 2 ms–2.
5.1
Draw a diagram to show the forces that act on the block while it accelerates upwards.
(3)
5.2
Calculate the tension in the cable while it accelerates upwards.
(5)
5.3
The crane motor then stops winding the cable. Explain why the block tends to continue
to move upwards. Name the law that you use to explain this.
(4)
[12]
6
QUESTION 6
Lusuko and Penny conducted an investigation to determine the coefficient of static friction, s,
between two wooden surfaces. They used the following pieces of equipment during their
investigation:

wooden table top

wooden block of mass 200 g

various mass pieces

Newton spring balance

light string
6.1
Describe the method they followed to produce the following results.
Mass of block (g)
Normal force (N)
Static friction (N)
200
1,96
0,6
400
3,92
1,2
600
5,88
1,8
800
7,84
2,4
1000
9,80
3,0
(4)
6.2
Use the graph paper to plot a graph of the results in the table. Place the normal force on
the x-axis and static friction on the y-axis.
(4)
6.3
Calculate the gradient of the graph.
(2)
6.4
State the coefficient of static friction, s, for the wooden surfaces.
(1)
6.5
Describe how you think the learners should adapt their investigation if they want to
determine the coefficient of kinetic friction, k.
(2)
Do you expect the value of the coefficient of kinetic friction, k, to be greater than or less
than the coefficient of static friction, s?
(2)
6.6
[15]
7
QUESTION 7
Notozi and Zimbini designed an experiment to investigate the acceleration, a, experienced by a
wooden trolley when pulled by a force, F.
They varied the force, F. For each value of F, they determined the acceleration, a, of the trolley.
They obtained the following results.
Force (N)
Acceleration (ms–2)
0,4
0,3
0,8
0,6
1,2
0,9
1,6
1,2
2,0
1,5
7.1
Mention ONE method they can use to vary the force, F.
(2)
7.2
Describe ONE method that they could use to determine the acceleration, a.
(2)
7.3
Draw a graph of the results they obtained.
(4)
7.4
Use the graph to calculate the value of the gradient of the graph. Identify the value that
the gradient of the graph represents.
(3)
The learners now apply a force of 2F to the trolley. Use your answer to question 7.4 to
calculate the new acceleration, a, of the trolley.
(2)
The learners now apply a force of 4F to the trolley. Without calculating the answer, use
your answer to question 7.5 to describe how the acceleration, a, changes as the force
applied changes.
(2)
7.5
7.6
[15]
8
QUESTION 8
A group of learners want to determine the weight of a metre stick using the principle of moments
of force. They set up the following apparatus.
The pivot supports the one end of the metre stick. The pivot is 1 cm from the edge of the metre
stick. A Newton spring balance supports the other end of the metre stick. The Newton spring
balance is at the 96 cm mark of the metre stick.
8.1
The learners must first ensure that the metre stick is exactly horizontal. Describe a
simple method that they can use to check that the metre stick is exactly horizontal.
(2)
Draw a force diagram to show the forces that act on the metre stick. Exclude the forces
that act at the pivot. Include the relevant distances in your diagram.
(4)
The reading on the Newton spring balance is 0,81 N. Calculate the weight of the metre
stick.
(5)
8.4
Calculate the mass of the metre stick.
(2)
8.5
Describe what the learners must do to ensure that their result is accurate.
(2)
8.2
8.3
[15]
9
QUESTION 9
A truck with a mass of 1 500 kg tows a car with a mass of 1 000 kg across a rough road surface,
as shown in the following diagram. The force of friction between the four wheels of the truck and
the road is 150 N. The force of friction between the four wheels of the car and the road is 100 N.
For the purpose of calculations, ignore the mass of the tow rope between the car and the truck.
9.1
Calculate the magnitude of the force, P, needed to give the truck and the car together
an acceleration of 1,6 ms–2.
(5)
9.2
Draw a labelled force diagram of the truck. Show all the forces that act on the truck.
(5)
9.3
Calculate the tension in the tow rope.
(6)
9.4
Explain how the acceleration of the truck and the car together changes if you take the
mass of the tow rope into account.
(3)
[19]
QUESTION 10
You tie two blocks together by a short length of very light string that does not stretch. The two
blocks have masses of 4 kg and 6 kg, as shown in the following diagram. A force of 84 N pulls
the 6 kg block to the right. There is a constant frictional force of 12 N that acts between the
surface and each of the two blocks.
10.1
Draw a labelled force diagram for each block. Indicate the frictional force (Ff), the
normal reaction force (N), the tension in the rope (T) and the force of attraction of each
block to the centre of the Earth (Fatt).
(6)
10.2
State Newton’s second law of motion in words.
(3)
10.3
Apply Newton’s second law of motion to calculate the acceleration of the system.
(6)
10.4
Determine the coefficient of kinetic friction, μk, between the surface and the 6 kg block.
(4)
10.5
If the string between the 2 blocks is cut. Draw the v-t graph for the two objects on the
same system of axis assuming no friction.
(5)
[19]
10
QUESTION 11
In rugby, a scrum consists of a group of eight players from each team. Each group of eight
players is a pack and each pack faces each other. Each pack pushes against the pack from the
opposing team to try and move them backwards. In a rugby match, the South African pack
exerts a force on the English pack. According to one of Newton’s laws of motion, the English
pack exerts an equal and opposite force on the South African pack.
11.1
Identify which of Newton’s laws of motion is referred to in the paragraph above.
(1)
11.2
Explain how the South African pack is able to move the English pack backwards.
(4)
[5]
QUESTION 12
3
7
A satellite has a mass of 1,5  10 kg. It orbits the Earth at a distance of 1,25  10 m from the
24
centre of the Earth, which has a mass of 6,0  10 kg.
12.1
Calculate the gravitational force that the Earth exerts on the satellite.
(5)
12.2
Decide whether the force exerted by the satellite on the Earth will be greater than,
smaller than or the same as the force exerted by the Earth on the satellite.
(1)
[6]
QUESTION 13
Most new models of cars have airbags as a standard safety requirement. Car manufacturers
design airbags to inflate when a car is involved in a collision.
13.1
State Newton’s first law of motion in words.
(3)
13.2
Name the property of matter to which Newton’s first law of motion relates.
(2)
13.3
Mention ONE other safety device that is fitted to cars to prevent injuries due to the
effects of Newton’s first law of motion.
(2)
[7]
11
QUESTION 14
An object of mass m rests on the surface of a planet of mass M.
14.1
14.2
14.3
14.4
Write an equation for the weight of the object in terms of m and g, where g is the
acceleration due to gravity on the surface of the planet.
(2)
Write the equation for the weight of the object in terms of M and R, where R is the
radius of the planet.
(2)
Combine the two equations in questions 14.1 and 14.2 to show that g does not depend
on m but only on M and R.
(3)
The mass of the planet is approximately
1
th the mass of the Earth. Its radius is
1
the
80
4
radius of the Earth. Use the equation you derived in question 14.3 to show that g at the
1
planet’s surface is about th of the value of g on the Earth.
5
(5)
[12]
QUESTION 15
A girl of weight 280 N sits on a swing. Her father pulls her backwards with a force of 120 N at
right angles to the rope, as shown in the following diagram.
15.1
Draw a labelled free-body diagram of all THREE forces that act on the swing’s seat.
(6)
15.2
Calculate the angle, , between the rope and the vertical when the father holds the
swing stationary.
(6)
[12]
12
QUESTION 16
A block of mass 5 kg remains stationary on a plane that is inclined at 30 to the horizontal, as
shown in the following diagram.
Draw a labelled force diagram to show the block’s weight and the components of its
weight parallel and perpendicular to the inclined plane. Your diagram does not need to
be to scale.
(4)
16.2
Calculate the values of the above two components of the block’s weight.
(6)
16.3
Calculate the magnitude and direction of the frictional force between the block and the
plane.
(2)
Calculate the coefficient of static friction, s, between the block and the plane.
(3)
16.1
16.4
[15]
QUESTION 17
A compressed spring joins two trolleys with masses of 2 kg and 3 kg. The trolleys move at a
velocity of 1,5 ms–1 to the left under frictionless conditions on a horizontal surface.
17.1
State the law of conservation of linear momentum in words.
(3)
The compressed spring between the trolleys is released. Immediately after the spring expands
fully, the velocity of the 3 kg trolley is 0,5 ms–1 to the right.
17.2
Say whether the total momentum of the system changes.
(1)
17.3
Calculate the velocity of the 2 kg trolley after the spring expands.
(6)
[10]
13
QUESTION 18
The following diagram shows two trolleys travelling east under frictionless conditions. The 1 kg
trolley moves at a velocity of 2 ms–1. The 2 kg trolley moves at a velocity of 0,5 ms–1. The two
trolleys collide and then continue to move as one unit (in other words, the trolleys are joined).
18.1
18.2
Name and state the law used to calculate the combined velocity of the trolleys after they
have collided.
(4)
Calculate the velocity of the trolleys joined together after the collision.
(7)
[11]
QUESTION 19
19.1
State the principle of conservation of momentum in words.
19.2
Two objects, A and B, with masses of 45 kg and 65 kg respectively, move towards each
other. Object A moves at a velocity of 10 ms–1 east, while Object B moves at a velocity
of 6 ms–1 west. They collide and stick together after the collision.The two objects are
initially 10m apart.
19.2.1 Calculate the time taken for the two to collide.
(3)
19.2.2 Calculate the velocity of the objects immediately after the collision.
(3)
(7)
A golf club exerts an average force of 3 kN on a golf ball of mass 46 g. The club is in contact
–4
with the ball for 5,0  10 s.
19.3
Calculate the magnitude of the change in momentum of the ball.
(4)
19.4
Calculate the speed of the ball as it leaves the club.
(4)
[18]
QUESTION 20
Sir Isaac Newton (1642 – 1727) was a well known English physicist, who did research on
motion. Newton studied the works of Aristotle, as well as the works of other scientists, at
the University of Cambridge. He formulated many laws, which we still use today. Newton’s
Second Law of Motion states: “The acceleration of a body is directly proportional to the
unbalanced force acting on it and inversely proportional to its mass.”
14
Two science learners, Steve and Charles, are doing experiments to verify Newton’s Second Law.
They accelerate a trolley, attached to a ticker timer and a ticker tape, along a horizontal surface.
They measure the accelerating force by means of a spring balance, which they have attached to the
trolley. They do several runs with the trolley, each time increasing the applied force. They record
their results:
ACCELERATION (m.s-2)
FORCE
(N)
5
4
3
2
1
0,600
0,455
0,315
0,175
0,035
20.1 Use their results and plot a graph of Force versus Acceleration.
(5)
20.2 Explain the position of the intercept of the graph on the x-axis.
(3)
20.3 Use the graph to determine the mass of the trolley.
(4)
20.4 If the experiment was repeated by using the same trolley on a much smoother surface, how
would a graph obtained from such an experiment differ from the graph obtained from the experiment
done by Steve and Charles?
(3)
QUESTION 21
A little boy plays with his toy train. He ties the engine to the first truck of the train, using a piece of
string. He ties a second piece of string to the engine. He pulls the train to the right on a horizontal
surface, with a force of 10 N. The masses of the engine and the truck are 1,8 kg and 1,4 kg
respectively. Frictional force of 2,4 N acts between the engine and the surface and a frictional force of
1,2 N acts between the truck and the surface.
14 N
18 N
10N
T
1,2N
2,4N
14N
18N
15
21.1 Draw two separate, labelled free-body diagrams, indicating all the forces acting on the truck and
on the engine.
(8)
21.2 Calculate the acceleration of the train.
(3)
21.3 Calculate the force that the engine exerts on the truck.
(4)
21.4 Calculate the coefficient of static friction for the engine on the surface.
(3)
QUESTION 22
A force F acts on a body and the body accelerates. If the mass of the body is doubled and the force is
halved, how would the acceleration of the body be affected?
(4)
Two mass pieces, 5 kg and 7 kg respectively, are
QUESTION 23
connected by an ideal string. The string is passed over a
pulley and the mass pieces hang down on either side of the
pulley. Initially, they are held stationary, both exactly 1,5 m
from the pulley. They are released simultaneously. How
long will it take for the 5 kg mass to strike the pulley?
5kg
7kg
QUESTION 24
A horse pulls a cart, C, mass 240 kg, attached to a log of wood, W, mass 80 kg, on a
horizontal road. W is tied to the back of C by means of an inelastic rope, which is
inclined at 30° to the horizontal. The horse applies a force of 170 N on cart C and the
system accelerates at 0,3 m.s-2 to the left. The force of friction on cart C is 40 N. The
rope has negligible mass.
170N horse
a = 0,3m.s-2
Cart C
240kg
30
80kg
16
wood
W
(7)
24.1 Draw a force diagram for cart C indicating ALL the forces on the cart.
(4)
24.2 Calculate the magnitude of the force which the rope exerts on C.
(8)
24.3 Calculate the magnitude of the frictional force on the wood W .
(6)
QUESTION 25
A spaceship, mass MS, is on its way to the moon from the earth. At a specific point of
its journey the earth, spaceship and moon are all in a straight line. The mass of the
earth is given as ME and the mass of the moon is given as MM. The centre of the
moon is a distance r from the centre of the earth.
25.1 State Newton’s Law of universal gravitation.
(4)
25.2. At a certain distance X from the earth the space ship experiences a net resultant force of zero.
taking into account the moon and the earth only, formulate an equation which indicates that the
distance X , from the earth, is independent of the mass of the spaceship Ms .
(4)
QUESTION 26
X
Y
F
2M
M
Two blocks x and y on a frictionless surface are in contact with
each other . The blocks are accelerated by a horizontal force
F. What is the magnitude of the force that Y exerts on X? (5)
17
QUESTION 27
A stationary police car of mass 1000kg is 90m behind a suspects car. The police gives chase at a
constant acceleration of 2ms-2 east, whilst the suspects drive at a constant velocity of 9ms-1 east.
27.1 Calculate how long it will take the police to catch the suspect.
(5)
27.2 If the police man applies his brakes after 15 seconds applying a force of 3000N, determine how
seconds is required to bring the car to rest.
(5)
QUESTION 28
Ice skating experts Jack and Jill approach each other at 7 m.s-1 and 5 m.s-1 respectively when they are
9m apart. They join hands and move off together.
28.1 Calculate the time taken for them to join hands.
(3)
28.2 Calculate the distance covered by the pair after they collide.
(5)
28.3 If the time of impact on collision is 0.05s , determine the force that Jack applies on Jill. (3)
QUESTION 29
The two masses 2kg and 4kg rest on a rough surface. They are attached to each other by a string
running over a pulley. They are pulled by a force of 24N to the right.
The frictional force between the 4kg mass and the surface is twice that of the frictional force between
the 2 blocks. If the acceleration of the system is 2 m.s-2 to the right , determine the magnitude of the
frictional forces between the surface and the block and that between the two block surfaces.
2kg
24N
4kg
18
QUESTION 30
The diagram below represents a block of mass M accelerating down an inclined plane angled at Ө degrees to
the horizontal. Assume the acceleration due to gravity is g (9.8 m.s-2 ).
M
Ө
30.1 Prove that the acceleration of the block , a , is independent of the mass M of the block. (5)
30.2
M = 2kg
M =1.5kg
300
30.2 Two masses of 2kg and 1.5kg are attached to each other by a string that runs over a
pulley. The plane is inclined at 300 to the horizontal .A frictional force exists between the 2kg
and the surface. If the acceleration of the system is 1.25m.s-2 determine the co-efficient of kinetic
between the 2kg mass and the Inclined plane .
(8)
19