Air Track SE - physics PDF

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Name: __Salan Bhattarai_

Date:2021/03/30

Student Exploration: Air Track Vocabulary: air track, approach velocity, conservation of energy, conservation of momentum, elasticity, kinetic energy, momentum, separation velocity, velocity

Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Imagine going to a bowling alley with a bowling ball and a ping pong ball. 1. Why is a bowling ball better for knocking down pins than a ping pong ball? Because bowling ball contains greater mass that could do more damage to the pins, but a ping pong ball will not cause much damage and won’t even cause the pins to fall because of its light mass compared to pins.

2. Which do you think would knock down more pins, a bowling ball moving 10 meters per second or a bowling ball moving 10 centimeters per second? A bowling ball moving at 10m/s would knock down more pins because it has higher velocity and is covering more distance in less time compared to 10cm/s. Because of it’s greater velocity, the force would be bigger to which will know more pins down. 3. What two factors seem to most affect the amount of damage that occurs in a collision? As I have described in question one and two about the impact of mass and velocity on knocking down pins, thus velocity and mass are two factors that affect the amount of damage in a collision. Greater mass and higher velocity= larger collision damage.

Gizmo Warm-up An air track is a device that helps scientists study motion. Air comes out of holes in the track, allowing the gliders to move with minimal friction. 1. On the Air Track Gizmo, click Play (

) to view a collision between the two gliders.

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What do you see? Both gliders have same mass and are travelling at opposite direction (one with positive and two with negative velocity). As they collide, they bounce back the way they came.

2. Click Reset ( ). The velocity (v) of an object describes its speed and direction. The velocity of each glider is indicated next to the v1 and v2 sliders. Click Play, and then click Pause ( ) just before the collision. A. What is the velocity of Glider 1? 5.0m/s B.

In which direction does Glider 1 move? From left to right or [E]

C.

What is the velocity of Glider 2? -5.0m/s

D.

In which direction does Glider 2 move? From right to left or [S]

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Activity A:

Get the Gizmo ready:

Momentum

 Click Reset.

Question: How does an object’s momentum change when it collides with another object? 1. Explore: The Gizmo allows you to adjust the mass and initial velocity of each glider. Set up each of the following scenarios, and describe what happens when the gliders collide. A. The gliders have the same mass but different velocities. When the velocities are different, the two gliders switch up their velocity once they collide. The one moving slower goes at a fast speed and the one moving fast goes slower after they collide. We can connect this to newtons third law which states every action has equal and opposite reaction. B. The gliders have the same mass and one glider is stationary. The moving glider stays stationary at rest when the collision occurs whereas the glider that was initially at rest moves towards right. We can see the transfer of energy from one glider to other. C. The gliders have the same speed (but moving in opposite directions) and different masses. The velocity of glider with greater mass decreases after the collison and moves back the same way it came whereas, the velocity of lighter glider increases after they collide and moves in opposite direction.

2. Calculate: An object’s momentum (p) describes how hard it is to stop. Momentum is equal to the product of mass and velocity: p = mv. If mass is measured in kilograms and velocity in meters per second, the unit of momentum is kilograms-meters per second, or kg•m/s. A. What is the momentum if the mass is 1.5 kg and the velocity is 4 m/s? P=mv =1.5 x 4 6kg*m/s Turn on Show numerical data and use the Gizmo to check your answer. B. How could you use the Gizmo to increase a glider’s momentum? Just use the sliders to increase the mass or velocity of gliders.

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3. Gather data: Click Reset. Set m1 to 3.0 kg and v1 to 2.0 m/s. Set m2 to 2.0 kg and v2 to -4.0 m/s. Fill in the left table, run the collision, and then fill in the right table. Before collision Glider

Glider 1

Glider 2

Mass

3.0 kg

2.0 kg

Velocity

2.0 m/s

-4.0 m/s

Momentum

6 kg•m/s

-8 kg•m/s

After collision

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Glider

Glider 1

Glider 2

Mass

3.0kg

2.0kg

Velocity

-2.8m/s

3.2m/s

Momentu -8.4 kg•m/s 6.4 kg•m/s m (Activity A continued on next page)

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Activity A (continued from previous page) 4. Calculate: To find the total momentum, add up the momentum of each glider. (Note: Pay attention to signs.) A. What was the total momentum of the two gliders before the collision? 6-8= -2 kg•m/s B. What was the total momentum of the two gliders after the collision? -8.4 - 6.4 = -2 kg•m/s. Turn on Show total momentum to check your answers.

5. Experiment: Click Reset. Set up three collisions using any combination of masses and velocities you like. (The only rule is that the gliders must collide.) Record the mass, velocity, and momentum of each glider before and after the collision. Then, find the total momentum. Remember to include units. Glider 1

Glider 2

Total momentum

m

v

p

m

v

p

Before collision

1kg

2m/s

2 kg•m/s

2kg

-3m/s

-6 kg•m/s

-4 kg•m/s.

After collision

1kg

-4.67 m/s

-4.67 kg•m/s

2kg

0.33m/ s

0.67 kg•m/s

-4 kg•m/s.

Before collision

2kg

4m/s

6 kg•m/s

3kg

0m/s

-1 kg•m/s

5 kg•m/s.

After collision

2kg

-2m/s

-4 kg•m/s .

3kg

3m/s

9.kg•m/ s

5 kg•m/s.

Before collision

3kg

3m/s

9 kg•m/s

2.5kg

-6m/s

-15 kg•m/s

-6 kg•m/s

After collision

3kg

5.18m/ s

-15.54 kg•m/s

2.5kg

3.82m/ s

-9.54 kg•m/s

-6 kg•m/s

6. Analyze: What do you notice about the total momentum of the two gliders? The total momentum of the two gliders before the collision is equal to the total momentum to two gliders after the collision.

7. Draw conclusions: The principle of conservation of momentum states that, in a closed system, the total momentum of all of the objects will remain constant. How do your experiments demonstrate conservation of momentum?

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The experiment demonstrates the conservation of momentum by illustrating how the momentum of gliders remained the same before and after collision and did not change. _________________________________________________________________________

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Activity B:

Get the Gizmo ready:  Click Reset.  Check that the Elasticity is set to 1.0.

Velocity

Introduction: When two gliders are moving toward each other, the relative speed they are moving together before the collision is called the approach velocity. Similarly, the speed at which the gliders are moving apart after the collision is described by the separation velocity. Each is equal to the difference in the gliders’ velocities: v(approach) = v1 – v2

v(separation) = v2′ – v1′

Question: What rule governs the velocities of two colliding objects? 1. Calculate: Set m1 to 3.0 kg and m2 to 1.5 kg. Set v1 to 4.0 m/s and v2 to -6.0 m/s. Pay attention to the signs of the velocities as you calculate them. A. What is the approach velocity of the two gliders? 10.0 m/s [4.0 – (-6.0) = 10.0] B. Click Play and then Pause after the collision. What is the velocity of each glider? Glider 1 velocity: -2.67m/s__

Glider 2 velocity: 7.33m/s

C. What is the separation velocity of the two gliders? 10.0 m/s [7.33 – (-2.67) = 10.0] D. What do you notice? The approach velocity is equal to separation velocity.

2. Experiment: Click Reset. Set up two collisions using any combination of masses and velocities you like. Calculate the approach velocity and separation velocity for each collision. Remember to include units. Glider 1

Glider 2

m

v

m

v

2kg

3m/s

3kg

-6m/s

After collision

2kg

-7.80 m/s

3kg

1.20m/ s

Before collision

1kg

4m/s

2kg

-2m/s

After collision

1kg

-4m/s

2kg

2m/s

Before collision

v(approach)

v(separation)

3-(-6) 9m/s

1.2-(-7.80) 9m/s

4-(-2) 6m/s

2-(-4) 6m/s

3. Analyze: So far, you have found that momentum is conserved in a collision. What else appears to be conserved? Explain your answer. The approach velocity is equal to separation velocity. The net velocities are conserved as the v approach is equal to v separation. (Activity B continued on next page)

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Activity B (continued from previous page) [Note: The following extension is designed as a challenge.] 4. Challenge: So far, you have found two rules that govern the behavior of the gliders before and after a collision. These two rules are expressed by the equations below. (Note: In each equation, a prime symbol (′) indicates “after the collision.”) Before collision Conservation of momentum:

After collision

m1v1 + m2v2 =

Approach velocity = separation velocity:

m1v1′ + m2v2′

v1 – v2

=

v2′ – v1′

If you are given the initial masses and velocities of the objects, you can use these two equations to solve for the two unknowns: v1′ and v2′. Try this in the space below. (Hint: Solve the second equation for v2′, and then substitute this expression into the first equation.)

v1′ = (m1v1 + 2m2v2 – m2v1) / (m1 + m2) v2′ = v1 + v1′ – v2

5. Solve: For each of the situations given below, determine the final velocity of each glider. Use the Gizmo to check your answers. (The Gizmo cannot be used to solve the last problem.) A. Glider 1 has a mass of 2.0 kg and a velocity of 2.6 m/s. Glider 2 has a mass of 3.0 kg and an initial velocity of -4.4 m/s. v1′ = -5.80m/s

v2′= 1.20m/s

B. Glider 1 has a mass of 0.5 kg and a velocity of 9.0 m/s. Glider 2 has a mass of 1.0 kg and an initial velocity of -9.0 m/s. v1′= -15m/s

v2′ = 3m/s

C. Glider 1 has a mass of 5.0 kg and a velocity of 15.0 m/s. Glider 2 has a mass of 6.0 kg and a velocity of -12.0 m/s. v1′= 14.45m/s

v2′ = 12.55m/s

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Activity C: Kinetic energy and elasticity

Get the Gizmo ready:  Click Reset.  Check that the Elasticity is set to 1.0.  Turn off Show numerical data for both gliders.

Introduction: The kinetic energy (KE) of an object is a measure of its energy of motion, measured in joules (J). Kinetic energy depends on both the mass and velocity of the object: KE = mv2 / 2 Question: What happens to the kinetic energy of a system during a collision? 1. Calculate: Set m1 to 3.0 kg and v1 to 2.0 m/s. Set m2 to 1.5 kg and v2 to -6.0 m/s. A. What is the kinetic energy of Glider 1? 6J

Glider 2? 27J

B. What is the total kinetic energy of both gliders? 33J

2. Run Gizmo: Turn on Show numerical data. Click Play and then Pause after the collision. A. What is the kinetic energy of Glider 1? 16.67J

Glider 2? 16.33J

B. What is the total kinetic energy now? 33J

3. Experiment: Click Reset. Set up two collisions using any combination of masses and velocities. Calculate the kinetic energy of each glider and the total kinetic energy. Remember to include units. Glider 1

Glider 2

m

v

KE

m

v

KE

Total KE

Before collision

2kg

4m/s

16J

3kg

-3m/s

13.50J

29.5J

After collision

2kg

-4.40 m/s

19.36J

3kg

2.60m/ s

10.14J

29.5J

Before collision

3kg

2m/s

6J

1kg

-6m/s

18J

24J

After collision

3kg

-2m/s

6J

1kg

6m/s

18J

24J

4. Summarize: The principle of conservation of energy states that in a closed system the total energy remains constant. How do your experiments demonstrate this principle? This experiment demonstrates the principle of conservation energy by showing that the total kinetic energy remains same before and after collision. (Activity C continued on next page)

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Activity C (continued from previous page) 5. Experiment: If the colliding objects are deformed in the collision, some of the kinetic energy is converted to heat and/or sound. The elasticity of a collision is related to the kinetic energy that is preserved in a collision. Set the Elasticity to a value less than 1.00 and run an experiment with any combination of masses and velocities. Record the results below. Remember to include units. Glider 1

Glider 2

m

v

KE

m

v

KE

Total KE

Before collision

2kg

4m/s

16J

3kg

-4m/s

24J

40J

After collision

2kg

-3.20 m/s

10.24J

3kg

0.80m/ s

0.96J

11.2J

6. Calculate: Elasticity is also related to the approach velocity and the separation velocity. A. What is the approach velocity in the example above? v(approach) = v1 – v2 = 4-(-4) 8m/s B. What is the separation velocity in the example above? v(separation) = v2′ – v1′ =0.80-(-3.20) 4m/s

C. What is the ratio of the separation velocity to the approach velocity? 8/4 or 1/2m/s D. How does the elasticity of the collision relate to this ratio? The elasticity for this experiment was set to 0.5 thus the elasticity of the collision directly related to the ratio which is v approach/vseperation as the ratio is ½ or 0/5. 7. Gather data: Repeat your experiment with several different values of Elasticity. In each experiment, record the approach velocity, separation velocity, and the ratio of the separation velocity to the approach velocity. Remember to include units. Trial

Elasticity

1

0.2

v(approach)

v(separation)

v(separation) v(approach)

v(approach)= v1 –v2

v(separation) = v2′ – v1′ -016-(-1.76)= 1.6m/s

1.6/8=0.2

4-(-4)= 8m/s

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2

0.8

4-(-4)= 8m/s

1.76-(-4.64) = 6.4m/s

6.4/8=0.8

3

0.6

4-(-4)= 8m/s

1.12-(-3.68) = 4.8m/s

4.8/8=0.6

8. Make a rule: Based on your table, how could you calculate the elasticity of a collision if you know the approach velocity and separation velocity of the colliding objects? To calculate the elasticity of a collision we can divide the separation velocity by approach velocity. Thus, the ratio of separation velocity to approach velocity is equal to the elasticity.

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