Physics Unit 5:
Momentum and
Collisions
Topic 5.1 – Momentum and Impulse
Topic 5.2 – Elastic Collisions
Topic 5.3 – Inelastic Collisions
Learning Goal: You will understand how two objects behave after they collide in an elastic
collision.
Success Criteria: You will know you have met the learning goal when you can calculate the
velocities of objects after they collide in an elastic collision.
Image from Bing Images
When objects collide, a variety of things can happen. They can stick together, they can shatter,
they can bounce off each other, they can deform, etc. In this topic, we’ll look at what happens
when two objects bounce off each other, otherwise known as an elastic collision.
A perfect elastic collision is where the object that collide are not deformed or altered in any
way. While no collisions are perfectly elastic, some come close, such as when two very hard,
touch objects collide. We’ll look at elastic collisions as though they are perfect.
Image from Bing Images
All collisions obey the law of conservation of momentum. In
elastic collisions, the objects don’t stick together. Momentum is
transferred from one object to another. We can thus write an
equation for the momentum of elastic collisions, keeping in mind
that momentum (p) is mass times velocity.
m1v1i + m2v2i = m1v1f + m2v2f
(1 and 2 refer to the two objects. i and f refer to initial and final.)
This equation means that the mass times the initial velocity of
object one plus the mass times the initial velocity of object two
equals the mass times the final velocity of object one plus the
mass times the final velocity of object two. Initial and final in this
case mean before and after the collision. The total momentum of
the system remains constant.
In this class, we will only deal with collisions in one dimension
(along a straight line). Note that in the picture on the right, one
ball would have a positive velocity and the other would have a
negative velocity since they are moving in opposite directions. As
a convention, left is negative and right is positive.
Image from Bing Images
Task 5.2.1 (12 points): Sketch the following elastic
collisions and calculate the wanted information.
a) Suppose two masses collide. If the 2kg mass
has an initial velocity of 4m/s and the 3kg mass
has an initial velocity of -5m/s, what is the final
velocity of the 2kg mass if after the collision, the
3kg mass is moving at 2.2m/s?
b) A tank launches a 25kg shell at 87m/s. It
collides with a 1.6kg bird flying at -7m/s. How fast
will the bird be flying after the collision if the shell
slows down to 75.93m/s? (This probably wouldn’t
be an elastic collision in real life)
c) You run into a stationary garbage can at
6m/s (look where you’re going next time). If after
the collision the garbage can moves at
7.3939m/s and you slow down to 1.3939m/s,
what is your mass if the garbage can is 38kg?
Image from Bing Images
Task 5.2.1 (12 points): Sketch the following elastic
collisions and calculate the wanted information.
d) Two pitchers throw baseballs at each other. If
the first pitcher throws the ball at 38m/s to the
right, and the second throws the ball at 45m/s to
the left, what is the velocity of the first pitcher’s ball
after they collide in midair the second pitcher’s
ball is moving at 38m/s to the right? Both balls
have masses of .142kg
e) A tennis ball (mass: .0572kg) collides with a
basketball (mass: .675kg). How fast must the tennis
ball have been moving before the collision if after
the collision, the tennis ball moves at 29.83m/s and
the basketball moves at 4.43m/s. The initial velocity
of the basketball is 8.4m/s.
f) You accidentally run into another runner on the
track. If your mass is 58kg and your initial velocity is
6.50m/s, how fast will you be moving after the
collision if the other runner, who is 49kg, goes from
4.70m/s to 6.65m/s?
Image from Bing Images
In elastic collisions, kinetic energy is conserved. Since kinetic energy (K) is ½mv 2, we can write:
½m1v1i2 + ½m2v2i2 = ½m1v1f2 + ½m2v2f2
The most useful implication of this fact is that we can combine it with the conservation of
momentum equation to solve for the final velocities of both objects when only the initial
velocities are known. Combining the equations with some algebraic manipulation yields:
v1f = [(m1 – m2)v1i + 2m2v2i]/(m1 + m2)
Use this equation to solve for one of the final velocities, then use this equation again (or the way
you already learned) to find the final velocity of the other object.
Image from Bing Images
Task 5.2.2 (6 points, 2 points each): Answer the
following questions (all are elastic collisions).
a) A 3kg ball rolling at 5m/s rolls up from
behind and collides with a 7kg ball rolling at
2m/s (note that both velocities are positive,
thus they are both moving in the same
direction). After the collision, what are the
velocities?
b) Two asteroids collide with each other head
on. If the first asteroid has a mass of 80,000kg
and a velocity of 375m/s and the second
asteroid has a mass of 120,000kg and a
velocity of -415m/s, what are their velocities
after the collision?
c) A helium atom with a mass of 6.64x10-27 kg
and a velocity of 68m/s collides with and
bounces off of an atom of neon with a mass of
3.32x10-26 kg and a velocity of -204m/s. What
are their velocities after they collide?
Image from Bing Images
Task 5.2.3 (4 points): Write a two-paragraph (4 sentences per paragraph) summary of
what you learned in this topic.
Images from Bing Images