Experiment 3E Collisions on Air-Track



Experiment 6: Collisions on an Air Track

Purpose

The purpose of this experiment is to study the Principles of Conservation of Momentum and Conservation of Kinetic Energy.

Apparatus

Air track with sparker and supplies (recording tape, sticking tape,

wooden sticks, etc.) Equal-arm balances (on the side)

|Theory |EQUATION (1) |

|(A) Conservation of Momentum |CONSERVATION OF MOMENTUM |

|In a collision of two objects like the air track gliders, their momenta | |

|are changed. However, the sum of the momenta of both objects (the Total | |

|Momentum) is conserved and stays the same as shown in Equation (1). | |

| |MA UiA + MB UiB = MA UfA + MB UfB |

| | |

| |MA, MB = masses of gliders |

| |UiA, UiB= their velocities before the collision |

| |UfA, UfB = their velocities after the collision |

| (B) Conservation of Kinetic Energy |EQUATION (2) |

|If the internal forces between the colliding objects are conservative, |CONSERVATION OF KINETIC ENERGY |

|then the Total Kinetic Energy will be conserved. If only kinetic energy | |

|is involved, an equation like Equation (2) applies. Collisions where the | |

|Total Kinetic Energy is conserved are called elastic collisions. | |

| | |

| |½ MA UiA2 + ½ MB UiB2 = |

| |½ MA UfA2 + ½ MB UfB2 |

| | |

| (C) Coefficient of Restitution If the internal forces between | |

|the colliding objects are dissipative (at least partially). |EQUATION (3) |

|the Total Kinetic Energy is not conserved, resulting in |COEFFICIENT OF RESTITUTION |

|inelastic collisions. To compare elastic and inelastic | |

|collisions, it is convenient to quote the Coefficient of |e = - ( UfB-UfA) |

|Restitution “e” given by (3). In elastic collisions, e = 1. | |

|If there is a loss of Total Kinetic Energy, then e ( 1. |(UiB-UiA) |

|The greatest possible loss occurs when e = 0 and the | |

|colliding objects stick to each other after the collision. | |

(D)Air Track: This is a device allowing gliders to move along the track supported by an air-cushion resulting in negligible friction. To measure the speed of the glider, a timing device (a sparker) is used which produces sparks at regular intervals.

Caution: Be careful when using this equipment. The high voltage produced by the sparker can be dangerous.

TURN THE AIR SUPPLY ON AND LEAVE IT ON THROUGHOUT THIS EXPERIMENT. Do not move the gliders along the track unless the air supply is on. The track is easily damaged by scratches, and it is expensive.

Preliminary Procedure: Testing the Air Track

(a) Gently place a glider on the track and release it from rest: the glider should remain motionless.

If the glider moves, the track is not horizontal. Call your instructor to adjust the track.

(b) Place a glider on the track and give it a moderate push: it should bounce many times off the ends of the track before appreciably slowing down (or stopping). If this test fails, it means that there is too much friction. If a glider jumps off the track or is dropped, it may be very slightly bent. You may not notice this, but it may fail to pass the above test. Call your instructor for adjustment.

(c) Attach about 50 cm of the recording tape, white side up, in the middle of the track. Place the glider near the left end of the track and hold it with the wooden stick, while your partner starts the sparker. Give the glider a moderate push to the right, creating a test run at constant speed. Your tape record should look like this:

. . . . . . . . . . .

Fig. 1 The Record of a Uniform Motion

(i) the dots on the tape should be sharp andnot smeared

(ii) no dots should be missing

ASK YOUR INSTRUCTOR TO APPROVE YOUR TEST-RUN BEFORE PROCEEDING

Procedure Part I: Elastic Collisions

(d) Use the heavier glider as Glider A. It should have a wire and a holder for additional mass to be attached to it. Measure and record its mass as MA under Run #1. Record the mass of the second glider (Glider B) as MB.

(e) Attach at least 100 cm of recording tape in the middle of the track. Place Glider A near the left end of the track and Glider B about 20 cm to the right of the midpoint of the tape. Hold Glider A with the wooden stick, with air supply on, start the sparker. Give glider A a moderate push to the right to achieve the collision. Keep the sparker on after the collision and stop it just before glider B rebounds from the right end of the track and collides again with Glider A.

To achieve good accuracy, make sure that UA is at least 30 cm/sec but avoid

excessive speeds. If the glider jumps off the track, it may be damaged:

CHECK YOUR TAPE RECORD FOR QUALITY. IF IN DOUBT ASK YOUR INSTRUCTOR.

(f) If the tape is good, label it as Run #1 and sign the tape. Make additional runs so that each partner has their own tape.

(g) Increase the mass of Glider A (check with your instructor for details) and repeat and (f) as Run #2. Record the new mass.

Procedure Part II: Inelastic Collisions

(h) Find Gliders A and B which have velcro on the ends facing each other. Measure and record MA and MB, as before, under Run #3. Make sure MA includes the pliable wire and the holder for additional masses.

(i) Follow the instructions under (e), but now Gliders A and B will stick together after the collision. Make one run for each partner.

(j) Increase the mass of Glider A (check with your instructor for details) and repeat (h) and (i) as Run #4.

Before you leave the Lab: All your tapes, properly labeled, and signed with your name, must be initialed by your instructor along with your data sheet. Make sure you understand how to process the data.

Lab Report

Part I:

(1) Your tape should look like this:

Ignore the collision region and, if confusing, the left and right ends of your tape (consult your instructor). Mark large intervals di before the collision and df after the collision as shown in Fig. 2. Write on the tape and in your report the number N of the intervals between dots. If an occasional dot is missing, fill it in. Measure di and df. Since the sparker produces a dot every 1/60 of a second, t = 1/60 • number of dots). Write the time and calculate UiA and UfA by dividing your measurements by the time.

(2) Copy and fill out Table #1 using the correct units. Show your calculations.

(i) UiA and UfA are obtained from your calculation in (1).

(ii) Find UfB by using Equation (1).

(iii) Calculate the total KE (Kinetic Energy) before and after the collision and enter

it in the table.

(iv) The % loss in KE should be calculated with respect to the

Total KE before. If there is a gain in KE, enter it with minus sign.

|TABLE # 1. ELASTIC COLLISIONS |

|RUN |

|# |

| | | |Measured |Theoretical |% Discrepancy |

|RUN |MA |MB |From Tape |UfA= MA . UiA |in UfA |

|# | | |UiA UfA |MA + MB | |

|3 | | | | | |

|4 | | | | | |

(5) How well do your results confirm the Principle of Conservation of Total

Momentum?

(6) Copy and fill out Table #3. Use the measured values of the intial and final VA.

|Table #3. INELASTIC COLLISIONS. |

RUN

# |MA |MB |UiA |UfA |е |Total KE

Before. . |Total KE

After |% Loss

in KE | |3 | | | | | | | | | |4 | | | | | | | | | |

Questions

(1) What are the theoretical values of the % loss in Total Kinetic Energy in runs #3 and

#4. (use the theoretical value of the final velocity).

(2) If a rubber ball is dropped from the height of 120 cm from the floor, and rebounds to a

height of 80 cm, what is the value of e? Show your reasoning.

(3) Can you conceive of a situation where the (internal) forces between the colliding

objects are conservative, but the collision is still inelastic (total kinetic energy is not

conserved)? If you do, give a practical example.

Attach your tapes to your report.

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