Physics 30: Module 2: Lesson 3
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MODULE 2: LESSON 3 COMPONENT COLLISION ANALYSIS WORKSHEET
Component analysis can be used to solve inelastic and elastic collisions in two dimensions. Below is an
example problem and solution for each type of collision. All directions are in the polar positive
specification.
Inelastic Collision in Two Dimensions - Complete number 1 and 3 other
questions 40 marks
Example Problem
A car with a mass of 1250 kg is travelling 18.0 m/s at 315°. It has an inelastic collision with a truck of
mass 1850 kg that was southbound at 15.0 m/s. Both the car and the truck stick together after the
impact. What was the velocity of the wreckage immediately after the collision?
First, find the x and y components of
the car’s momentum.
Second, find the y component of the
truck’s momentum. (The x
component will be zero because it is
not moving in the x direction.)
Physics 30: Module 2: Lesson 3
Now, total the x components and y
components of the momentum
before the collision.
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Px total = px1 + px2
Px total = (+1.59 x 104 kgm/s) + (0)
Px total = +1.59 x 104 kgm/s
Note: The most common mistake in P
y total = py1 + py2
these problems is forgetting to
Py total = (–1.59 x 104 kgm/s) + (–2.78 x 104 kgm/s)
specify the positive (+) or negative (–
Py total = – 4.37 x 104 kgm/s
) directions in the addition!
Add the total x and y components as
vectors.
polar positive direction = 360° – 70.0° = 320°
Finally, divide the total momentum
by the total mass to determine the
total velocity.
Elastic Collision in Two Dimensions
Example Problem
A car with a mass of 1350 kg is travelling 20.0 m/s at 125°. It has an elastic collision with a truck of
mass 2650 kg that was travelling at 18.0 m/s at 205°. If the truck has a velocity of 17.0 m/s at 155°
immediately after the collision, what is the velocity of the car?
To solve this problem, follow the same general steps as in an inelastic collision—there are just more
momentums to add. The example problem solution is based on the following steps:
 Find the x and y components of momentum for each object both before and after the collision.
Physics 30: Module 2: Lesson 3
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 Apply the conservation principle to each direction independently:
 x momentum before = x momentum after
 y momentum before = y momentum after
 Manipulate the conservation principle in terms of the unknown variables and solve.
Step 1: Determine the x and y momentum of the
car before the collision.
Step 2: Determine the x and y momentum of the
truck before the collision.
Step 3: Determine the x and y momentum of the
truck after the collision.
Physics 30: Module 2: Lesson 3
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Step 4: Apply the conservation principle, and
manipulate for the unknown variables.
Step 5: Determine the x and y components of the car’s momentum after the collision by applying the
conservation principle from step 4.
Step 6: Add the x and y components of the car’s
momentum after the collision as vectors to
determine the overall momentum:
polar positive direction = 180° + 43.7° = 224°
Physics 30: Module 2: Lesson 3
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Step 7: Finally, divide the car's final momentum
by the car's mass to determine its final speed,
and note the direction for the final velocity.
Obviously, this is a very long process. But if one of the objects involved in the collision is at rest or
travelling in only an x or a y direction, the process gets much shorter. This example problem illustrates
the most complex scenario. The problems on the worksheet can be solved by an application of the
process. Most problems will not, however, always require so many calculations.
Component Collision Analysis Worksheet
As part of your Module 2: Lesson 3 Assignment. Complete the odd numbered questions. Show all
your work. Demonstrate that you have used the GRASP form. Of course, these questions provide you
with the practice that you need to successfully complete this course. You should respond to all of the
questions and place the answers in your course folder.
The answer(s) for each question follows in brackets.
1.
5 marks
Add the following momenta to determine the resultant momentum for the following
collisions:
a. 50 kg•m/s at 45° and 59 kg•m/s at 90°
Answer:
5 marks
b. 175 kg•m/s at 100° and 144 kg•m/s at 180°
Answer:
5 marks
c. 1.6 kg•m/s at 280° and 5.5 kg•m/s at 190°
Answer:
5 marks
d. 1659 kg•m/s at 260° and 3125 kg•m/s at 190°
Answer:
Physics 30: Module 2: Lesson 3
5 marks
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e. 3.9 kgm/s at 10° and 3.7 kgm/s at 70°
Answer:
5 marks
2.
A billiard cue ball with a mass of 0.60 kg and an eight ball with a mass of 0.55 kg
are rolled toward each other. The cue ball had a velocity of 3.0 m/s at 360°, and
the eight ball had a velocity of 2.0 m/s at 90o. After the collision, the cue ball moves
off at a velocity of 2.8 m/s at 105o. What is the velocity of the eight ball?
Answer:
5 marks
3.
A proton heading due north is struck by a neutron heading at 320°. The neutron
bounces off with a heading of 50°. The initial speed of the proton was 2800 m/s,
and the neutron was travelling at 2900 m/s. After the collision, the speed of the
neutron is unchanged. If a neutron has the same mass as a proton, what is the
final velocity of the proton?
Answer:
5 marks
4.
A car is entering the freeway. The merge lane has a heading of 260°. The car has
an inelastic collision with a truck that had a velocity of 80 km/h at 270°. The car had
a mass of 1400 kg and a speed of 75 km/h. The mass of the truck was 1800 kg.
a. What is the initial common velocity of the car and truck after the collision? (
Answer:
b. If the wreckage takes 6.0 s to come to rest, how far from the point of impact
will they come to rest if we assume a uniform negative acceleration?
Answer:
c. What force did each vehicle apply to the other if the actual time of impact
was 0.010 s?
Answer:
Physics 30: Module 2: Lesson 3
5 marks
5.
7
Air hockey puck A, travelling at a velocity of 0.33 m/s at 360o, elastically strikes air
hockey puck B, which was travelling at 0.66 m/s at 295°. After the collision, puck A
has a velocity of 0.17 m/s at 288°. If the mass of A was 628.0 g and the mass of B
was 529.0 g, what was the final velocity of B?
Answer:
5 marks
6.
Two identical objects, each with a mass of 367 g, collide elastically. Object A was
travelling at 30 cm/s at 145°. Object B was at rest. After the collision, object A has
a velocity of 30 cm/s at 176°. What is the velocity of B?
Answer:
Once you have completed all of the questions, submit your work to your teacher.