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Copy of 2DCollisions SE COLLEGE PHYSICS
Physics for Electronics (Seneca College)
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Name:
Daniella Bafas
Date:
21/11/21
Student Exploration: 2D Collisions
Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.
Vocabulary: center of mass, conservation of energy, conservation of momentum, elasticity, kinetic energy,
momentum, speed, vector, velocity
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Gizmo Warm-up
Objects collide all the time, but often with very different results. Sometimes
colliding objects will stick together. Other times, they will bounce off each other
at an angle. What determines how objects will behave in a collision? You can
use the 2D Collisions Gizmo to find out.
Note the arrows, or vectors, on each puck. Click Play (
).
1. How does the direction and length of its vector relate to the motion of a puck?
The direction and the length of the vector determine the velocity of the puck.
2. The velocity (speed and direction) of each puck is described by components in the i and j directions. The
symbol for velocity is v. (Vector quantities are shown in bold.)
A.
Which component represents movement in the east-west direction?
Compon
ent “i”
B.
Which component represents movement in the north-south direction?
Compon
ent “j”
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3. The speed (v) of a puck is equal to the length of its velocity vector. To calculate the speed of a puck with a
velocity of ai + bj, use the Pythagorean theorem:
Set the velocity of the blue puck to 12.00i + 5.00j m/s. What is its speed? v=
Activity A:
Elastic collisions
13.00m/s
Get the Gizmo ready:
● Click Reset. Make sure Elasticity is set to 1.0.
● Set the blue puck’s velocity to v = 4.00i + 3.00j
and the gold puck’s velocity to v = 0.00i – 4.00j.
Introduction: An object’s elasticity describes how readily it returns to its original shape after it has collided
with another object. In a perfectly elastic collision (in which elasticity equals 1), the two colliding objects return
to their original shape immediately after the collision takes place.
Question: What is conserved during an elastic collision?
1. Calculate: The kinetic energy (KE) of an object is a measure of its energy of motion. The equation for
kinetic energy is: KE = mv2 ÷ 2, and the unit for kinetic energy is the joule (J). In the equation, m represents
an object’s mass and v represents its velocity.
A. Calculate the kinetic energy of each puck. (Note: The mass of the pucks can be found on the
CONTROLS pane, and the magnitude of the pucks’ velocities (v) can be found at the bottom of the
SIMULATION pane.)
Blue puck KE =
62.5 J
Gold puck KE =
24.0 J
B. Add the kinetic energy of the blue puck to that of the gold puck to find the total kinetic energy for the
system.
Total system KE =
86.5 J
2. Compare: Turn on Velocity vectors during motion. Click Play and observe the pucks.
A. Calculate the final kinetic energy of the two pucks and the total system.
Blue puck KE =
11.45
J
Gold puck KE =
75.0 J
Total system KE =
86.5 J
Use the CALCULATION tab to check your work.
B. How did the kinetic energies of the two pucks change, and how can you explain these changes?
The kinetic energy of the blue puck decreased whereas, the kinetic energy of golden
puck increased after the collision.
C. How did the total system kinetic energy before the collision compare to that of after
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the collision?
The total kinetic energy before the collision equaled to the kinetic
energy after the collision. The kinetic energy was conserved during
the collision.
3. Make a rule: Complete the sentence: During an elastic collision, the total kinetic energy of
the system
is conserved.
. This rule is part of the law of conservation of energy.
4. Calculate: It takes force to deflect or stop a moving object. Momentum (p) is a measure of an object’s
tendency to continue moving in a given direction. The formula for momentum is
p = mv and the unit is newton-seconds (kg•m/s). Click Reset. Select the CONTROLS tab.
Because momentum has direction, it can be described in both the i direction and j direction. Calculate the
initial momentums (pay attention to +/- signs):
Blue puck:
p in i direction =
20.0 kg m/s
p in j direction =
15.0 kg m/s
Gold puck:
p in i direction =
0.00 kg m/s
p in j direction =
12.0 kg m/s
Total system:
p in i direction =
20.0 kg m/s
p in j direction =
3.00 kg m/s
5. Calculate: Click Play and observe the pucks collide. Calculate the final momentums:
Blue puck:
p in i direction =
0.25 kg m/s
p in j direction =
10.7 kg m/s
Gold puck:
p in i direction =
19.8 kg m/s
p in j direction =
-7.71 kg m/s
Total system:
p in i direction =
20.0 kg m/s
p in j direction =
3.00 kg m/s
Use the CALCULATION tab to check your answers.
6. Compare: Look at the momentum values you calculated for before and after the collision.
A. What did you notice about the total system momentum in the i direction?
The total system momentum in the “i” direction is the same before and after
collision.
B. What did you notice about the total system momentum in the j direction?
The total system momentum in the “j” direction is the same before and after
collision.
During an elastic collision, the total momentum in both the i direction and the j direction remains the
same. This rule is part of the law of conservation of momentum.
7. Compare: Click Reset. Select the MOMENTUM tab. Set up several different collisions. Click Play. Then,
compare the gray Total momentum vector Before and After the collision.
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A.
How do the Before and After vectors compare?
The vectors from before and
after are equal in magnitude.
B.
What does this observation confirm?
The observation confirms that
the momentum and kinetic
energy before and after are
equal in magnitudes which
conclude that the momentum
and kinetic energy are
conserved.
Activity B:
Inelastic
collisions
Get the Gizmo ready:
● Click Reset.
● On the CONTROLS tab, turn on Puck trails.
Question: What is conserved during an inelastic collision?
1. Observe: Use the Gizmo to set up a new collision. Run the simulation first with an Elasticity of 1.0. Then,
run the simulation with an Elasticity of 0.0.
What was the effect of decreasing the elasticity?
Upon decreasing its elasticity, the final velocity of the pucks decreases compared to the
initial velocity.
2. Predict: In activity A, you found that both total kinetic energy and total momentum are conserved in a
perfectly elastic collision. How do you think decreasing the elasticity of a collision will affect the total
momentum and total kinetic energy after the collision?
The total momentum will remain the same however; the kinetic energy will decrease after
the collision. In a perfect elastic collision the kinetic energy and momentum were conserved
however, in a non elastic collision, the kinetic energy will decrease and the momentum will
be conserved.
3. Experiment: Move the blue puck to point (-4.0, -6.0). Set its Initial velocity to v = 3.00i + 6.00j. Set the
Initial velocity of the gold puck to v = 0.00i – 6.00j. Use the Gizmo’s Elasticity slider and CALCULATION
tab to complete the table.
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Elasticity
Stage
Blue puck
p
(kg•m/s)
Gold puck
Total
p
TKE (J)
p (kg•m/s)
TKE (J)
(kg•m/s)
Total
TKE (J)
Before
15.00i +
30.00j
112.50
0.00i-18.0
0j
54.00
15.00i+
12.00j
166.50
After
9.31i +
15.69j
33.30
5.69i +
27.69j
133.20
15.00i+
12.00j
166.50
Before
15.00i +
30.00j
112.50
0.00i-18.0
0j
54.00
15.00i +
12.00j
166.50
After
10.74i 4.27j
13.35
4.26i +
16.27j
47.15
15.00i +
12.00j
60.49
Before
15.00i +
30.00j
112.50
0.00i 18.00j
54.00
15.00i +
12.00j
166.50
After
12.16i +
7.15j
19.90
2.84i+
4.85j
5.26
15.00i +
12.00j
25.16
1.0
0.5
0.0
4. Analyze: Study the data you collected in the table on the previous page.
A. In an inelastic collision, how did the total momentum (p) of the system change?
The momentum remained the same from before and after the collision.
B. In an inelastic collision, how did the total kinetic energy of the system change?
The total kinetic energy decreased from before and after the collision.
C. How were the inelastic collisions different from the elastic collision?
In an elastic collision both momentum and kinetic energy were conserved, however;
in an inelastic collision only momentum is conserved and the total kinetic energy
decreases.
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5. Make a rule: Complete the sentence: During an inelastic collision, the total momentum of the
system is
conserved
, while kinetic energy is
not conserved
6. Infer: Why do you think some of the kinetic energy is lost during an inelastic collision?
After an inelastic collision the objects travel in the same direction which results in some of
the kinetic energy being converted to other types of energy like thermal energy or sound
energy.
7. Think about it: Suppose a meteorite collided head-on with Mars and becomes buried under Mars’s surface.
What would be the elasticity of this collision? Explain your answer.
The elasticity of this collision will be 0. If it was a perfectly elastic collision then the
meteorite would bounce back resulting in a conservation of momentum and kinetic energy.
However, in this situation, the meteorite is being buried under the surface resulting in a loss
of the total kinetic energy.
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Get the Gizmo ready:
Activity C:
Center of mass
● Click Reset. Turn on Center of mass trail.
● Move the blue puck to point (-4.0, -6.0). Set its
Initial velocity to v = 3.00i + 6.00j.
● Move the gold puck to point (4.0, -6.0). Set its
Initial velocity to v = 3.00i + 6.00j.
Introduction: Suppose you tried to balance a hammer on one finger. If you placed your finger halfway down
the handle, the hammer would fall because the head is much heavier than the rest of the hammer. Instead, you
would have to place your finger near the head to balance the hammer perfectly. The point where an object
balances is called its center of mass.
Question: How can you find the center of mass of a system?
1. Identify: The center of mass for the system of two pucks is where the balancing point would be if a
weightless rod connected the pucks. Set the mass of both pucks to 5.0 kg.
What do you think are the coordinates of the center of mass of the two pucks?
The coordinates of the center of mass of the two pucks would be (0, -6).
2. Compare: Click Play. The teal blue trail represents the trail of the system’s center of mass. How does the
center of mass trail compare to the trails of the two pucks?
The centre of the mass trail is parallel to the trails of the two pucks.
3. Observe: Click Reset. Change the Blue puck mass to 10.0 kg. Click Play. How did this affect the center of
mass?
The centre of the mass trail is more inclined towards the blue puck because the mass is
larger than that of the gold puck.
4. Calculate: Click Reset. Set the Elasticity to 1.0. Move the blue puck to (2.0, -12.0) and change its mass to
6.0 kg. Move the gold puck to (12.0, -4.0) and change its mass to 1.5 kg.
A. About where do you think this system’s center of mass is?
(7, -8)
B. The i coordinate of the center of mass can be found using the following equation:
C. What is the i coordinate of the center of mass?
The i coordinate of the centre of
mass is 4.
The same equation can be used to find the j coordinate of the center of mass.
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D. What is the j coordinate for this system?
-10.4
5. Run Gizmo: Click Play. The first teal dot on the center of mass trail indicates the original position of the
center of mass.
Were your calculations correct? If not, what were the actual coordinates?
My calculations were
correct.
6. Compare: Click Reset. Set the blue puck’s velocity to v = 0.00i + 6.00j and the gold puck’s velocity to v =
-8.00i + 0.00j. Click Play.
A. Describe the trail of the center of mass. How is it different from the pucks’ trails?
The trail of the centre of the mass is linear and it does not change before or after the
collision. After the collision the puck’s trail changes directions due to an elastic
collision however; the centre of the mass trail stays the same.
B. Based on the spacing of the trail marks, compare the velocity of the center of mass before and after
the collision.
The velocity of the centre of the mass trail before and after collision is constant.
There is no increase or decrease and it stays constant throughout.
7. Observe: After a collision, the velocities of the pucks will almost always change, but the velocity of the
center of mass remains constant.
A. Why do you think the velocity of the center of mass does not change?
The velocity of the centre of the mass does not change because the trail of the
centre of the mass is based on the mass used. The mass used stays the same
before and after the collision, therefore; the velocity remains constant. The velocity of
the puck may change due to the collision however; the mass used is the same
throughout.
B. Select the MOMENTUM tab. How does the center of mass trail compare to the gray arrow
representing the total momentum of the system?
The centre of the mass trial is equivalent to the total momentum of the collision.
C. Click Reset, and try out various initial settings that result in a collision. For each of these collisions,
compare the center of mass trail to the arrow representing the total momentum of the system. What
trend do you see?
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The total momentum of the system is equivalent to the centre of the mass trail.
D. What is the relationship between the velocity of a system’s center of mass and the law of
conservation of momentum?
The relationship between the law of conservation of momentum and velocity of the
centre of the mass trail is that they both remain constant before and after the
collision. No mass or momentum is lost during the collision and therefore; they both
represent a linear relationship.
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