Grade 12
Physical Sciences
Mechanics
(Momentum)
Lesson Description
In this lesson we will:
 Learn that an object’s momentum is the “amount of motion” it
has due to its mass and velocity.
 Show that momentum during collisions and explosions is
conserved by the transfer of momentum between objects.
 Find out whether collisions are elastic or inelastic by using
calculations.
 Use the principle of conservation of momentum to solve
problems.
Key Concepts:
 Momentum – the momentum of an object is the amount of
motion it has.
o Momentum is calculated by multiplying the object’s mass
(in kg) and its velocity (in m.s-1).
o Momentum is measured in kg.m.s-1 and is a vector
quantity.
o Direction plays an important role in an object’s
momentum.
p = m.v
 Impulse – impulse is the amount of change in motion an
object has because it experiences a force for some time.
o Force is a vector, therefore, the force can be positive or
negative to show its direction.
o One way to think of impulse is the way objects swap or
trade momentum with one another.
Page 2 of 12
o When objects with momentum touch:
 They exert forces on one another.
 Newton’s third law states that the force between
them is exactly the same, but in opposite
directions.
 They touch each other (and exert the same force
on one another) for the same amount of time.
 This will cause an equal but opposite change in
their momenta, conserving the total momentum in
the system.
Δp = FΔt
F = m(vf – vi)/Δt
 Principle of Conservation of Momentum
o Total momentum in a closed system remains constant in
both magnitude and direction.
o The principle of conservation of momentum is used to
solve problems based on collisions.
 For two objects that separate after collision.
 For two objects that couple after collision.
 For two coupled objects that separate after an
explosion.
 Elastic collision – a type of collision where kinetic
energy is conserved, i.e. kinetic energy before
collision is equal to kinetic energy after collision.
No loss in energy is encountered.
 Inelastic collision – a type of collision where kinetic
energy is not conserved.
K = ½ mv2
Page 3 of 12
 How to answer momentum questions
o Step 1 – Diagram & Direction
 Draw a diagram showing objects before and after
collision – remember to show direction – choose
which direction is positive.
o Step 2 – Conservation Equation
 2 objects before and after collision
pi = pf
m1vi1 + m2vi2 = m1vf1 + m2vf2
 2 objects before collision and 1 object after collision
pi = pf
m1vi1 + m2vi2 = (m1 + m2)vf
Page 4 of 12
 1 object before explosion and 2 objects after
explosion
pi = pf
(m1 + m2)vi = m1vf1 + m2vf2
Terminology:
 System – the collection of objects in question.
 Momentum – the amount of motion a body has due to its
mass and velocity.
 Conservation of Momentum – the total linear momentum of
an isolated system will remain the same.
 Impulse – the change in an object’s momentum due to a force
being exerted on it for a time.
 Collision – the rapid striking of two or more objects together.
 Explosion – the sudden, forceful separation of objects.
 Elastic collision – collision where kinetic energy is
conserved.
 Inelastic collision – collision where kinetic energy is lost.
Page 5 of 12
QUESTIONS: (Conservation of Momentum)
1. Two shopping trolleys, X and Y, are both moving to the right
along the same straight line. The mass of trolley Y is 12 kg
and its kinetic energy is 37,5 J.
a. Calculate the speed of trolley Y.
b. Calculate the speed of trolley X before the collision.
c. Calculate the magnitude of the force that trolley X exerts
on trolley Y.
2. A net force F acts on each of two isolated objects, P and Q,
as shown below. The mass of Q is three times that of P.
Ignore the effects of friction.
If the rate of change of momentum of object Q is x, then what
is the rate of change of momentum of object P?
Page 6 of 12
3. During an investigation a police officer fires a bullet of mass
15 g into a stationary wooden block, of mass 5 kg, suspended
from a long, strong cord. The bullet remains stuck in the block
and the block-bullet system swings to a height of 15 cm above
the equilibrium position, as shown in the diagram below.
Effects of friction and the mass on the cord may be ignored.
a. State the law of conservation of momentum in words.
b. Use energy principle to show that the magnitude of the
velocity of the block-bullet system is 1,71 m.s-1
immediately after the bullet struck the block.
c. Calculate the magnitude of the velocity of the bullet just
before it strikes the block.
d. The police officer is pushed slightly backwards by the
butt of the rifle, which he is holding against his shoulder,
whilst firing the rifle. Use the relevant law of motion to
explain why this happens.
Page 7 of 12
4. A truck of mass 24 tons moves to the right at 10 m.s-1.
Calculate the momentum of the truck.
5. A tennis ball of 500 g is thrown towards a wall at 12 m.s -1.
What is the momentum of the tennis ball?
6. A 4 kg object moving towards the north at 6 m.s -1 decreased
its velocity to 3 m.s-1 while moving in the same direction.
a. Calculate the change in momentum of the object.
b. If it took the object 2 seconds to change its velocity, what
is the magnitude of the force that caused the change in
momentum?
7. A 0,4 kg ball travels at 20 m.s-1 towards a bat and it is hit back
at a velocity of 30 m.s-1. Calculate the force exerted by the
bat on the ball if the time of contact is 0,01 seconds.
8. In a railway shunting yard, a locomotive of mass 4 000 kg
travels to the east at 1,5 m.s-1 and collides with a stationary
goods wagon of mass 3 000 kg. The two separate after the
collision, and the goods wagon moves to the east at 2,8 m.s -1.
a. Calculate the magnitude and direction of the velocity of
the locomotive immediately after the collision.
b. Name and state in words the law you used to answer (a).
9. A trolley with a mass of 8 kg is moving on a horizontal
frictionless surface at 4 m.s-1. A 5 kg bag of bird feed is
allowed to fall perpendicularly onto the trolley.
a. Calculate the velocity of the trolley and the bag after the
bag was placed onto the trolley.
b. Determine whether the collision between the trolley and
the bag was elastic or inelastic.
Page 8 of 12
10.
New cars have a crumple zone to help minimise injuries
during accidents. In addition seat belts, airbags and
padded interiors can reduce the chance of death or
serious injury.
a. Use principles in physics to explain how airbags can
reduce the chance of death or injury.
b. In a crash test, a car of mass 1,2 x 103 kg collides with a
wall and rebounds. The initial and final velocities of the
car are 12 m.s-1 to the left, and 2 m.s-1 to the right
respectively. The collision lasts 0,1 s. Calculate the:
i. Impulse of the car during the accident.
ii. Average force exerted on the car.
c. How will the magnitude of the force exerted on the car
be affected if the time interval of the collision remains
0,1s, but the car does not bounce off the wall? Write
down only INCREASES, DECREASES or REMAINS
THE SAME. Explain your answer.
Remember that impulse is equal to the change in momentum.
If you use the change in momentum to work out the impulse,
the units must be N.s even though you used mass and the
change in velocity!!
Page 9 of 12
11.
Collisions happen on the roads in our country daily. In
one of these collisions, a car of mass 1 600 kg,
travelling at a speed of 30 m.s-1 to the left, collides headon with a minibus of mass 3 000 kg, travelling at 20 m.s-1
to the right. The two vehicles move together as a unit in
a straight line after the collision.
a. Calculate the velocity of the two vehicles after the
collision.
b. Do the necessary calculations to show that the collision
was inelastic.
c. The billboard advert below advertises a car from a
certain manufacturer.
Use your knowledge of momentum and impulse to justify
how the safety features mentioned in the advertisement
contribute to the safety of passengers.
Page 10 of 12
12.
The most common reasons for rear-end collisions are
too short a following distance, speeding and failing
brakes. The sketch below represents one such collision.
Car A of mass 1 000 kg, stationary at a traffic light, is hit
from behind by Car B of mass 1 200 kg, travelling at 18
m.s-1. Immediately after the collision Car A moves
forward at 12 m.s-1.
a. Assume that linear momentum is conserved during the
collision. Calculate the speed of Car B immediately after
the collision.
b. Modern cars are designed to crumple partially on impact.
Explain why the assumption made in QUESTION 12(a)
may NOT be valid in this case.
c. A traffic officer appears at the scene of the accident and
mentions the dangers of a head-on collision.
He
mentions that for cars involved in a head-on collision, the
risk of injury for passengers in a heavier car would be
less than for passengers in a lighter car. Use principles
of physics to explain why the statement made by the
traffic officer is correct.
Page 11 of 12
13.
Two boys, Franck and Mandla, have masses of 50 kg
and 80 kg respectively. They stand on a stationary
trolley of mass 180 kg. The trolley is free to move in a
horizontal plane either to the left or to the right. The
boys simultaneously jump off the trolley in opposite
directions from each end of the trolley. Both the boys
leave the trolley with an initial speed of 3 m.s -1 relative to
the ground.
a. Calculate the magnitude and direction of the velocity at
which the trolley starts to move immediately after the
boys have jumped off the trolley.
b. Give a reason why the velocity of the trolley calculated in
13(a) does not remain constant after the boys have
jumped off.
c. Explain, using Newton’s second Law, why the trolley
moves in the direction as calculated in question 13(a) as
above.
d. The time it takes for Mandla to push against the trolley
with his legs is 0,2 s. During this time the trolley exerts a
force on Mandla. Calculate the magnitude of the force
the trolley exerts on Mandla during the time it takes for
Mandla to push against the trolley.
e. Explain why Mandla accelerates towards the right if the
force exerted on Mandla by the trolley and the force
Mandla exerts on the trolley has the same magnitude but
act in opposite directions to each other.
Page 12 of 12