Experiment 4 - California State Polytechnic University, Pomona



Experiment 6

Conserved Quantities

|Equipment in the lab |Equipment to check out |

|Computer |2 Pasco cars (one red, one blue) |

|Laser gate assembly |2 Pasco masses (with felt) |

|Lab pole frame |1 extra rectangular unlabeled mass |

|Meter stick |2 threaded rods |

| |Caliper |

INSERT PHOTOGRAPH OF SETUP

Introduction

In this experiment, you will investigate three types of collisions between two cars. You will measure the initial and final momenta of each car and initial and final kinetic energies of each car to determine if momentum and/or mechanical energy is conserved.

The computer will assist you by measuring the speed of the cars involved in the experiments.

Conservation of Mechanical Energy

Theory

If the net work done on an object is done by conservative forces, then mechanical energy is conserved. Mechanical energy is the sum of the kinetic and potential energy. Our experiment will consist of two cars moving horizontally. Therefore, the gravitational potential energy of the car-earth system will remain constant. Changes in mechanical energy will be solely reflected through changes in the kinetic energy of the cars.

Conservation of Momentum

Theory

If there are no external forces acting on a system of particles (or if the external forces sum to zero), then the total momentum of the system is conserved. That is, the total momentum of the system doesn’t change in time.

For our first collision, one car will start from rest, and the other will be pushed into it. After the collision, the two cars rebound from one another, as shown in figure 1. Let m2 be the mass of the car that starts at rest and m1 the mass of the car that is initially moving with a veloctiy of [pic]. Let the final velocities of the two cars be [pic] and [pic]. The initial momentum before the collision is [pic], and the final momentum after the collision [pic].

Examining figure 1, momentum conservation dictates that,

[pic] (1)

The v's without the vector symbols represent the speeds as opposed to the velocities of the cars.

You will compare the momentum before the collision, [pic], and the momentum after the collision, [pic], and see if they are equal, within experimental uncertainty.

For our second collision, one car will start at rest, and the other will be pushed into it. After the collision, the two cars will stick together, as shown in figure 2. Again, let m2 be the mass of the car that starts at rest and m1 the mass of the car that is initially moving.

Examining figure 2, momentum conservation dictates that,

[pic] (2)

You will compare the momentum before the collision, [pic], and the momentum after the collision, [pic], and see if they are equal, within experimental uncertainty.

For our third and final collision, both cars will start at rest, and a triggered spring mechanism will subsequently launch the cars away from one another, as shown in figure 3 (An analogy to this situation two stationary figure skaters that suddenly push off from one another). The initial momentum before the collision is 0, and the final momentum after the collision [pic].

Examining figure 3, momentum conservation dictates that,

[pic] (3)

You will compare the momentum before the collision, 0, and the momentum after the collision, [pic], and see if they are equal, within experimental uncertainty.

Procedure

Unlike for the rest of experiments this quarter, for this experiment, each table of 4 students will work together as one team. For each collision, one computer and laser-gate assembly may be used to measure the speed of one of cars and the other computer and laser-gate assembly may be used to measure the speed of the other car. You will be using the program "energy" to collect your data. The menu should be self-explanatory. The metal rod is screwed into the hole in the center of the car. As the car passes under the laser-gate, the vertically oriented rod passes through the gate, and the time of gate blockage is measured. The width of the rod is divided by this time, and the resulting speed is displayed on the screen. Note: THESE CARS ARE EXPENSIVE. Do not let the cars fall off the table and hit the ground!

a) To check if the laser gate is working, type "t". The program samples the detector once every second and displays if the gate is blocked or unblocked.

b) To set the number of data points that will be collected, type "n".

c) To change the rod thickness, press "z".

d) To take data, press "d".

Experimental Considerations

For each collision, we are assuming one dimensional motion. Therefore, the laser-gates should be carefully positioned so that the path of the laser is perpendicular to the path of the car. Also, prior to each collision, the cars must be oriented along the same line so that their subsequent motion following the collision will remain along that same line. To obtain accurate speeds, you must carefully measure the width of each rod, using the calipers, and enter this rod thickness into the computer.

Preliminary measurements - to determine how well these experiments will adhere to the example of a system in the absence of external forces, set up your laser-gates at a distance of about 40 cm apart and push one of the cars and measure its speeds at each gate. The two speeds will differ due to friction or an unbalanced gravitational force (both external forces). Record data for at least 4 trials, over a range of speeds. You can then use these results to ascertain an appropriate speed which will limit the effects from external forces.

Measure the total mass of each car and its added mass. The blue car (m1) will be used with one added mass, a labeled Pasco mass (and the rod). The red car (m2) will be used with two added masses, a labeled Pasco mass and an unlabeled mass (and the rod).

Experimental Procedure – Part 1 - Bouncing Collision

Use the red car as the initially stationary car.

Position one of the laser gates so that you can measure the speed of the blue car as it travels toward the red car and its recoil speed after it bounces from the red car. In order for the cars to bounce, release the spring plunger to its full extension on the blue car. It is very important that you measure the blue car's speed before the plunger makes contact with the red car and after it is completely separated from the red car.

Position the second laser gate so that you can measure the speed of the red car after it is hit by the blue car and completely separated from it.

You should try a few practice runs until you feel comfortable with your technique.

Record data for three trials.

Experimental Procedure – Part 2 - Sticking Collision

Again, use the red car as the initially stationary car.

Position one of the laser gates so that you can measure the speed of the blue car as it travels toward the red car. Make sure that the plunger is pushed all the way in and is flush with the front of the car. For the cars to stick together, the velcro on one car must line up with the felt on the other car. Again, it is very important that you measure the blue car's speed before the it makes contact with the red car.

Position the second laser gate so that you can measure the speed of the both cars after they stick together.

As before, you should try a few practice runs until you feel comfortable with your technique.

Record data for three trials.

Experimental Procedure – Part 3 - Cars launched from rest.

Position the plunger on the blue car so that it is in its fully cocked position. Place the red car next to it (end to end and touching). Position the laser gates so they can measure each car's speed when they become fully separated.

To launch the cars, use a pointed object (like your pen) to push the release button. Try to do it quickly so that you don't add any extra force to the blue car after it is launched.

Practice this procedure until you feel comfortable with your technique.

Record data for three trials.

Data Analysis

Part 1 - Bouncing Collision

1. Display your data for the first collision in a table similar to table 1.

2. Compare the initial and final momenta (for example, determine the percent differences).

3. Is the momentum before equal to the momentum after the collision within the uncertainties of your measurements? (To answer this question, it will useful to examine the percent differences you measured in your preliminary measurements of the blue car as it slowed down due to friction or unbalanced gravitational forces).

4. Calculate and display the kinetic energies of the cars in a table similar to table 2.

5. Compare the initial and final kinetic energies (for example, determine the percent differences).

Table 1. Mass, speed and momentum data for the bouncing cars collision

|Trial |Mass m1 |Mass m2 |Speed |Speed |Speed |total initial |total final |

| |(units) |(units) |v1i |v1f |v2f |momentum |momentum |

| | | |(units) |(units) |(units) |(units) |(units) |

|1 | | | | | | | |

|2 | | | | | | | |

|3 | | | | | | | |

Table 2. Kinetic energy data for the bouncing cars collision

|Trial |kinetic energy KE1i |kinetic energy KE1f |kinetic energy |total intial kinetic |total final kinetic |

| |(units) |(units) |KE2f |energy (units) |energy (units) |

| | | |(units) | | |

|1 | | | | | |

|2 | | | | | |

|3 | | | | | |

Part 2 - Sticking Collision

6. Display your data for the second collision in a table similar to table 1, but appropriately adapted to display the pertinant information for the cars launched from rest.

7. Compare the initial and final momenta.

8. Is the momentum before equal to the momentum after the collision within the uncertainties of your measurements? (Again, it will useful to examine the percent differences you measured in your preliminary measurements of the blue car as it slowed down due to friction or unbalanced gravitational forces).

9. Calculate and display the kinetic energies of the cars in a table similar to table 2 (but again, adapted for the sticking collision).

10. Compare the initial and final kinetic energies.

Part 3 - Cars Launched from Rest

11. Display your data for the third collision in a table similar to table 1, but appropriately adapted to display the pertinant information for the launched cars.

12. Compare the initial and final momenta (here it will be most useful to find the percent differences between the magnitude of the final momenta of the two cars)

13. Is the momentum before equal to the momentum after the collision within the uncertainties of your measurements?

Questions

1. Gravity and the normal forces on the cars are external forces on the system. Why don't these forces preclude momentum conservation?

2. In which of the first two collisions is kinetic energy more conserved?

3. If kinetic energy was lost, where did it go? That is, what type of energy did it transform into?

Notes

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