The Air Track

The Air Track
Elastic Collisions

http://www.msu.edu/user/brechtjo/physics/airTrack/airTrack.html

Name ______________________________________ Hour __________

    This applet simulates collisions in one dimension. To run a simulation select one of the scenarios in the drop down menu and hit "Go". Press "Stop" at any time to pause the simulation. Pressing "Go" will restart it at that point. To create your own simulation, choose that option from the drop down menu, and two windows will appear that will allow you to edit the carts' properties.

    You may also edit their initial velocities and masses in the appropriate fields at the top, drag the carts to any position on the track, and edit "alpha". "Alpha" is a measure of the elasticity of a collision. An alpha value of one indicates an elastic collision, in which no kinetic energy is lost. Balls on a billiard table exhibit collisions that are nearly elastic. An alpha value of zero is a perfectly inelastic collision, in which the two colliding objects stick together after colliding. Colliding blobs of putty would exhibit perfectly inelastic collisions. Much of the energy in such a collision is converted to internal vibrations or heat.

Scenario #1:
     Elastic collision between Carts of Equal Mass

Applet Settings:

Alpha Setting

Red Mass

Red Velocity

Blue Mass

Blue Velocity

1.0

1

+100 m/s

1

0.0 m/s

Calculate the following initial values before running the simulation:

Initial Momentum - Red

Initial Momentum - Blue

Total Initial Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

Press "GO" and watch the simulated collision. Press "STOP" before the blue cart strikes the right side bumper. Record the velocity of red cart and the blue cart after the collision.

Red Cart Velocity = ___________ Blue Cart Velocity = ___________

(Note: Indicate the cart's direction with a + or - sign.)

Calculate the following final values after the collision:

Final Momentum - Red

Final Momentum - Blue

Total Final Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

What is the relationship between the initial and final momentums?

Describe the motion of the red and blue cart before and after the collision?

Scenario #2:
            Elastic collision Mass of Carts are Unequal.

Applet Settings:

Alpha Setting

Red Mass

Red Velocity

Blue Mass

Blue Velocity

1.0

3

+100 m/s

1

0.0 m/s

Calculate the following initial values before running the simulation:

Initial Momentum - Red

Initial Momentum - Blue

Total Initial Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

Press "GO" and watch the simulated collision. Press "STOP" before the blue cart strikes the right side bumper. Record the velocity of red cart and the blue cart after the collision.

Red Cart Velocity = ___________ Blue Cart Velocity = ___________

(Note: Indicate the cart's direction with a + or - sign.)

Calculate the following final values after the collision:

Final Momentum - Red

Final Momentum - Blue

Total Final Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

What is the relationship between the initial and final momentums?

Describe the motion of the red and blue cart before and after the collision?

What is the nature of an elastic collision?

Scenario #3:
            Elastic Collision - Both Cart in Motion and of Equal Mass

Applet Settings:

Alpha Setting

Red Mass

Red Velocity

Blue Mass

Blue Velocity

1.0

1

+100 m/s

1

-100.0 m/s

Position the red cart at the 40 cm mark and the blue cart at the 60 cm mark. Note the location point of impact when the collision occurs.

Calculate the following initial values before running the simulation:

Initial Momentum - Red

Initial Momentum - Blue

Total Initial Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

Press "GO" and watch the simulated collision. Press "STOP" before the carts strikes the side bumper. Record the velocity of red cart and the blue cart after the collision.

Red Cart Velocity = ___________ Blue Cart Velocity = ___________

(Note: Indicate the cart's direction with a + or - sign.)

Calculate the following final values after the collision:

Final Momentum - Red

Final Momentum - Blue

Total Final Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

What is the relationship between the initial and final momentums?

Describe the motion of the red and blue cart before and after the collision?

Where was the point of impact? _________ cm

Scenario #4:
                Elastic Collision - Both Cart in Motion with Unequal Mass

Applet Settings:

Alpha Setting

Red Mass

Red Velocity

Blue Mass

Blue Velocity

1.0

3

+100 m/s

1

-100.0 m/s

Position the red cart at the 40 cm mark and the blue cart at the 60 cm mark. Note the location point of impact when the collision occurs.

Calculate the following initial values before running the simulation:

Initial Momentum - Red

Initial Momentum - Blue

Total Initial Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

Press "GO" and watch the simulated collision. Press "STOP" before the carts strikes the side bumper. Record the velocity of red cart and the blue cart after the collision.

Red Cart Velocity = ___________ Blue Cart Velocity = ___________

(Note: Indicate the cart's direction with a + or - sign.)

Calculate the following final values after the collision:

Final Momentum - Red

Final Momentum - Blue

Total Final Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

What is the relationship between the initial and final momentums?

Describe the motion of the red and blue cart before and after the collision?

Where was the point of impact? _________ cm

Scenario #5:
            Elastic Collision - Both Cart in Motion with Unequal Mass and Speed

Applet Settings:

Alpha Setting

Red Mass

Red Velocity

Blue Mass

Blue Velocity

1.0

3

+100 m/s

1

-50.0 m/s

Position the red cart at the 20 cm mark and the blue cart at the 80 cm mark. Note the location point of impact when the collision occurs.

Calculate the following initial values before running the simulation:

Initial Momentum - Red

Initial Momentum - Blue

Total Initial Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

Press "GO" and watch the simulated collision. Press "STOP" before the carts strikes the side bumper. Record the velocity of red cart and the blue cart after the collision.

Red Cart Velocity = ___________ Blue Cart Velocity = ___________

(Note: Indicate the cart's direction with a + or - sign.)

Calculate the following final values after the collision:

Final Momentum - Red

Final Momentum - Blue

Total Final Momentum

P_r = m_r^.V_r

P_b = m_b^.V_b

P_tot = m_r^.V_r + m_b.V_b

kg^.m/s

kg^.m/s

kg^.m/s

What is the relationship between the initial and final momentums?

Describe the motion of the red and blue cart before and after the collision?

Where was the point of impact? _________ cm

Summary: Describe the main ideas learned in this activity regarding initial and final total momentum in elastic collisions.

Alpha Setting	Red Mass	Red Velocity	Blue Mass	Blue Velocity
1.0	1	+100 m/s	1	0.0 m/s

Initial Momentum - Red	Initial Momentum - Blue	Total Initial Momentum
P_r = m_r^.V_r	P_b = m_b^.V_b	P_tot = m_r^.V_r + m_b.V_b
kg^.m/s	kg^.m/s	kg^.m/s

Final Momentum - Red	Final Momentum - Blue	Total Final Momentum
P_r = m_r^.V_r	P_b = m_b^.V_b	P_tot = m_r^.V_r + m_b.V_b
kg^.m/s	kg^.m/s	kg^.m/s

The Air Track Elastic Collisions

The Air Track
Elastic Collisions