PHYS 111A-008 Lab 126: Conservation of Momentum and Impulse-Momentum Theorem
Lab 126: Conservation of Momentum and Impulse-Momentum Theorem
Professor Siliang Wu
March 28, 2013
- To verify the conservation of momentum for fully elastic and totally inelastic collisions:
- To verify the Impulse- Momentum Theorem.
For a body of mass m moving with velocity v, its linear momentum p is defined as
p ⃗=mv ⃗
According to the law of conservation of momentum, linear momentum of a system may change only if there is a net external force acting on this system, that is momentum of a system is conserved when there is no net external force acting on it. Collisions between the elements of a system don’t change the total linear momentum of the system (normal forces acting during the collision are “internal” forces).
For an external force F acting during time interval the impulse J is defined as
According to Newton’s laws of motions, changing the motion of an object requires the application of net external force. This leads to the Impulse-Momentum Theorem:
In states that the amount of the momentum change of an object in time interval t equals to the impulse of the net external force acting on this object during this time interval.
There are three types of collisions: fully elastic collision where both momentum and kinetic energy are conserved amid collision; inelastic collision where momentum is conserved while kinetic energy is not; totally inelastic collision where momentum is conserved while kinetic energy is not, and the two objects stick together after the collision so their final velocities are the same.
For any type of collision, as long as the system may be considered isolated, the total momentum of a system is conserved, that is the total momentum just before the collision equals the total momentum just after the collision.
In this lab, you will measure the glider velocities before and after collisions (both fully elastic and totally inelastic) on a frictionless air track and verify the conservation of momentum for the system of two gliders. In addition, you will directly measure the impulse of a collision between the glider and the probe and compare it with the change in the momentum of the glider to verify the Impulse-Momentum Theorem applying in the glider.
Part I. Conservation of Momentum in Elastic Collisions
An elastic collision will occur when M1, the lighter glider with no added mass, initially passes through the first photo gate making an elastic collision with a heavier glider of mass M2. Glider M1 will then rebound from the collision passing back through the first photogate while the heavier glider moves through the second photogate. The photogates will measure the times for each glider to pass thorough the photogate and allow measurement of the velocity for both gliders separately.
- Weigh the gliders without any added mass on them, but be sure to include the yokes, and record the value in Data Table 1.
- Check to ensure that the air track is leveled before each experiment by observing for any motion of the gliders.
- Set up the two gliders with the rubber band yokes to be used to create the elastic collision.
- Prepare the glider with glider M2 between the photogates and M1 outside photogate1. Add an additional 100g of weight to glider M2 and make sure that collision (contact) between the two gliders takes place only while they are both between the gates (do a test run to be sure).
- Best results are obtained by measuring the velocities immediately before and after the collision, not 20 or 30 cm later!! So do not keep the photogates too far from each other.
- Connect photogate1 to port DG1 and photogate2 to port DG2 of ULI interface.
- Open LoggerPro file, press the Collect button then push the glider M1 button when both gliders are outside the gates to finish the experiment.
- The velocities for both gliders before and after collision will be displayed on the screen. Record data in Data Table I. in order to get correct values of velocities; make sure to load the correct object length in the software. To do so, go to Setup/Data Collections/Sampling/Length of object for LoggerPro file or Data/User Parameters/Photogate Distance1 & Photogate Distance2 for LabPro file, there is an alternative way to do it: go to Experiment/Set Up Sensors/Show All Interfaces, then lick the photo gate icon in DIG/SONIC1 and DIG/SONIC2, and choose Set Distance or Length.
- Now add an additional 100-g mass to glider 2 and repeat the experiment. Record data.
- Finally, observe the collisions when gliders 1 and 2 have identical masses. Record data.
- For each of the three collisions, compute the momentum and kinetic energy before and after the collisions. Click Microsoft Excel Data Table and use the Excel worksheet for the calculations. Verify that momentum and kinetic energy are conserved.
Part II. Conservation of Momentum in Inelastic Collision
Glider M2 will initially be at rest. In this part of the lab, you will use the motion detector since we have only one moving object to track.
- Set up the motion detector at one end of the air track and connect it to Port 2 on ULI interface. Make sure it is properly aimed at the reflector which is now to be placed at the end of glider M1.
- Place a needle tip on glider M1 and a wax receptacle on the other one to ensure that the two gliders stick together after the collision. Weigh both gliders, record values in Data Table II.
- Disconnect and remove the photo gates since the sound reflector is too large to pass under them.
- Open file Lab 126_Part 2 in NJIT folder. Test the sensor to be sure that it picks up the reflected signal from the glider. Click the Collect button to start the experiment. Push glider M1 in the direction of M2.
- Observe the velocity of the glider M1 before the impact when it is moving alone, and after the impact when it is moving with the second glider. Read the values of velocity before (initial velocity) and after (final velocity) the collision.
- Repeat this experiment for several different added masses on the glider.
- Record your data in Data Table II.
- Click Microsoft Excel Data Table 2 to compute the momentum and kinetic energy before and after the collision using Excel worksheet for each collision. Compute the amount and percentage of energy lost momentum “lost” during collision. Verify that momentum is conserved while kinetic energy is not conserved in inelastic collision.
Part III. Impulse-Momentum Theorem
In this experiment we will use the force probe to measure the force acting on a glider as it rebounds off the sensor of the force probe.
- Connect Force Probe to DN1 of ULI interface and Motion Detector to Port2 of ULI interface. For LabPro interface, connect Force probe to CH1 and Motion Detector to DIG/SONIC1.
- Attach a rubber band yoke to a glider and weigh it, record value (M) in Data Table III.
- Open LoggerPro file lab126_Part3 in NJIT folder. Calibrate the Force Probe. Your force probe must be calibrated before use.
- Click the Collect button to start experiment. Push the glider in the direction of the force probe. Make sure that the force probe won’t move amid collision. Your computer should be displaying the velocity, acceleration and force graph.
- Observe the force pulse during the impact and the change in velocity of the glider as it rebounds. The collision should last about 0.2 sec. Calculate integral of ( this is impulse J) using the software capability: Click on the Force vs. Time graph, select the area around the force peak by dragging the dashed rectangle then click the Integral button. Record the initial velocity V, final velocity V’, and impulse J in Data Table III.
- Repeat this experiment with several different glider masses.
- For each trial with different glider masses, calculate the momentum and its change for the glider before and after colliding with the force probe. Click “Microsoft Excel Data Table” and use the Excel worksheet to do the computations.
- Compare the impulse J with the change in momentum (find % difference). Verify the Impulse-Momentum Theorem.
Mass of glider M1 plus any added mass Mass of glider M2 and any added mass
: Velocity of Glider M1 right before collision: Velocity of Glider M1 right after collision
: Velocity of Glider M2 right after collision
Discussion and Questions:
- In Part I. Calculate the percentage of momentum and kinetic energy “lost” during the collision. What are the possible sources that cause the loss? Where did the “lost” energy go?
- In Part II. Show that the fractional kinetic energy loss is and compare this fraction with your observed fractional energy loss.