Head-on Collision Assignment
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School
Centennial College *
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Course
307
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
2
Uploaded by PrivateMoosePerson1066
Head-on collision assignment
NAME:
This assignment requires you to predict possible outcomes resulting from a head-on collision involving two masses. All equations derived will be based on the assumption that we are working in a closed system. There will be no outside forces impacting on this collision process. Use the following symbols to denote the physical quantities given below.
Mass of incident object: m
1
Mass of object initially at rest: m
2
Speed of incident object prior to collision: v
1,i
Speed of m
1
after the collision: v
1,f
Speed of m
2
after the collision: v
2,f
The diagram below shows the pre-collision configuration of the system of the two masses.
For the purposes of this exercise, you may assume that there is no friction and no energy associated with a rotating body. Consider the bodies to be sliding along the surface. In a typical laboratory setting involving a collision of macroscopic objects, we would have data knowledge of the two masses. Our goal is to derive a formula for each of the two post-collision speeds in terms of the masses (which we can assume to be known through measurement), and the speed of the incident mass (which we will assume we can control using our lab equipment).
Answer the following questions using the symbols defined for this problem
.
Please answer all questions directly on this document. Do not upload or attach photos of your work. Make sure your typing or handwriting is neat.
Due date: March 24, 2024 at 11:59 pm.
PART ONE – Derivation of the formula for the final speeds of each object
1.
Write the linear momentum equation for this collision. 2.
Write the conservation of energy equation for this collision, assuming that this collision is
perfectly elastic. A real-life good approximation of an elastic collision would be a collision of two snooker balls. At this point in the exercise, you will have two equations (momentum and energy) in two unknowns (
v
1,f
and v
2,f
).
3.
Using algebraic techniques, determine the post-collision velocities of each mass. Since one of the equations is linear and the other equation is quadratic in the unknowns, you will need to solve this two-equation system using algebraic skill beyond the linear algebra techniques you are familiar with. The skills required are not beyond first-year college algebra.
PART TWO - Interpretation of results
Based on the answers you derived in Part One, answer the following questions.
4.
(a) What are the values of the post-collision speeds of the two masses if they are equal. Give your answers in terms of m
1
, m
2
, and v
1,i
.
(b) Explain in words what an observer would see regarding the behaviour of the masses after the collision.
5.
Explain in words what an observer would see if m
1
> m
2
. Specifically, state the direction of motion of each object after the collision.
6.
Explain in words what an observer would see if m
1
< m
2
. Specifically, state the direction of motion of each object after the collision.
7.
What is the direction of motion of each object after the collision if m
1
>>> m
2
? The symbol “>>>” means “very much greater than”. The implication is that m
1
would be several orders of magnitude greater than m
2
. Estimate the post-collision speed of each object in terms of v
1,i
. Hint: Think of a bowling ball colliding with a ping pong ball initially at rest.
8.
What is the direction of motion of each object after the collision if m
1
<<< m
2
? The symbol “<<<” means “very much less than”. The implication is that m
1
would be several orders of magnitude less than m
2
. Estimate the post-collision speed of each object in terms of v
1,i
. Hint: Think of a ping pong ball colliding with a bowling ball initially at rest.
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