Linear Air Experiment

Foundation Mechanics

H10FM1

Laboratory 2

UNIVERSITY OF NOTTINGHAM FOUNDATION MECHANICS CONSERVATION OF LINEAR MOMENTUM Aims To investigate the Law of Conservation of Linear Momentum. Apparatus Linear air track; blower unit; 3 x vehicles (one lighter than the others); magnetic buffers; plastic buffers; buffer with needles and clamps; 2 x photodiode gates, (one master and the other a slave); 2 x retort stands; Unilab Motion QED timer; ruler; plasticine; weighing scales; power supply capable of supplying 12 V. The blower unit supplies air to the track which flows through the small holes, thus providing a “cushion of air” for the vehicles to ride on with little (or no) friction. The vehicles have a card (of fixed length, usually 200 mm) placed into the slot on the top. As the vehicle approaches the photodiode gate, the card will cut the beam; this will start the timer. The vehicle will then traverse the photodiode gate and the card will then open the light path once more; this will stop the timer. Thus the time taken for the card to cut and then make the beam is measured and the velocity of the vehicle can be established. The velocity of the vehicle may be determined by dividing the length of the card by the time taken to cut and make the beam. On the Unilab Motion QED, the velocity can be determined directly. Master photodiode

Figure 1

Slave photodiode

Arrangement of the air track, vehicles and photodiodes

Conservation of linear momentum

1

Foundation Mechanics

H10FM1

Laboratory 2

Electrical connections required between the photodiodes and Unilab Motion QED timer. Power Supply

Unilab Motion QED timer

Master Photodiode

Slave Photodiode

DIN socket cables Figure 2

Electrical connections required

1.

Use the two cables with DIN sockets to connect a) the master photodiode to the slave photodiode b) the slave photodiode to the Unilab Motion QED timer

2.

Connect the power supply to the Unilab Motion QED timer

Procedure a)

Initial set-up 1.

Weigh one of the vehicles and record its mass. The measured mass should be of the vehicle complete with mask and whatever trimming weights have been added.

2.

Since we want the collisions to happen in the absence of all external forces, it is important that the track be perfectly horizontal and as frictionless as practical. To check the condition of your track send one glider to your right and note the time it takes to cross each of two photocells placed about 750 mm apart supported by retort stands.

Conservation of linear momentum

2

Foundation Mechanics

3.

H10FM1

Laboratory 2

Now set up the Unilab Motion QED timer. With the power supply on, ensure that the Unilab QED Motion timer shows “select” on the display. Press select (S button) until the option to measure speed appears and then press enter (E button). The device will now ask for how many readings you require. Press select (S) until the display shows “readings = 2” and then press Enter/Display (D). You are going to use 2 readings on this initial test. Now you will be asked to select the size of your mask. This has to be a whole number of centimetres, going from 0 – 9 in steps of 1 cm and then in steps of 10 cm. Measure the length of your mask (usually 20 cm) and press select (S) until the correct size is displayed. Press Enter/Display (D) when complete. Unfortunately, if you make a mistake, it is easier to switch off the power and start again. The display now ask you to press go (the G button) when you are ready to start the test. To ensure the device is working, simply pass your hand infront of one of the photodiodes twice. The measurements should be made and can be displayed using the Enter/Display button (D). Check you have two readings. To repeat a set of readings, simply press the Enter/Display button again to display the menu “< G > < S > < D >”. When you are ready for the next test press (G).

4.

Put on the air supply to the air track and launch one of the vehicles up the track and record the two speeds.

5.

Repeat step (4), but launch the vehicle in the opposite direction. Record the two speeds again.

6.

The difference between the two speeds divided by the speed it crossed the first photocell will give you the fraction of the momentum lost due to friction and gained (or lost) because of gravity.

Conservation of linear momentum

3

Foundation Mechanics

b)

H10FM1

Laboratory 2

Elastic collision between two vehicles, one initially at rest. 1.

Place the elastic band catapult at one end of the air track.

2.

Equip two vehicles with the card in the slots on the top, and test to ensure that they cut the light beam. Place the photodiode gates around 750 mm apart. Ensure they can pass without disturbance along the air track.

3.

Put the two magnetic buffers, one on each of the vehicles, so that the buffers are facing each other on the track. The magnetic buffers will repel each other on “impact”. Counterbalance the magnetic buffers with the brass buffers.

4.

Weigh the vehicles and record their masses. The measured masses should be of the vehicles complete with masks and whatever trimming weights have been added.

5.

Place one of the vehicles between the two photodiodes (see Figure 1) and about one vehicle length from the photodiode gate furthest from the launching end; try to ensure it is stationary before the impact (but don’t hold it!).

6.

Set up the Unilab Motion QED timer as described in the previous section, but now you want to measure 3 readings (so enter “readings = 3” when prompted, but otherwise the instruction are the same)

7.

When ready, press go (G) and launch the second vehicle towards the stationary one using the elastic band catapult.

8.

After impact and you have three readings (try to ensure the once stationary vehicle only gives you its FINAL velocity and doesn’t re-cross the photodiode), note the three speeds (and change these into velocities by thinking about the direction the vehicles were moving).

9.

Swap over the two vehicles, so the stationary one now becomes the launch vehicle and visa versa. Repeat the test.

10.

Try the experiment using the other vehicle. One of them is considerably lighter than the other two. You should aim to obtain a series of at least six different experimental conditions!

11.

If time allows, try adding additional masses EVENLY to both vehicles using the plasticine, ensuring that the vehicles are balanced (don’t dig into the air track) to obtain a range of different initial masses of both vehicles.

Conservation of linear momentum

4

Foundation Mechanics

c)

H10FM1

Laboratory 2

Inelastic collision between two vehicles, one initially at rest

This experiment is similar to (b), except the magnetic buffers are replaced by a buffer containing a needle (be careful – needles are sharp) clamped in it in one vehicle and brass buffers filled with plasticine in the other vehicle. Upon impact, the vehicles should join together. Theory Conservation of linear momentum If there is no external impulse applied to the body (or system of bodies) then the total linear momentum of the body (or system) remains constant in magnitude and direction. This is known as the Principle of Conservation of Momentum. It holds only if:a) there is no external impulse (i.e. no externally applied force) b) the total mass remains unaltered As before, this is a principle and not a mathematically proven fact; it is based on numerous experiments and observations over many years, and better men that the likes of us have not proved it wrong (yet?). Application to the collision of two bodies Consider the situation where a body A (of mass m1) moving with an initial velocity u1 collides with a second body B (of mass m2) moving with an initial velocity u2. During the impact there is an impulse (equal to F t) exerted by one body upon the other.

Velocity U1 A Mass m1

Velocity U2 m1 U1

B Mass m2

m2 U2

BEFORE IMPACT F t

F t IMPACT

Velocity V1 A Mass m1

Velocity V2 m1 V1

AFTER IMPACT

Conservation of linear momentum

5

B Mass m2

m2 V2

Foundation Mechanics

H10FM1

Laboratory 2

If the time t of the impact is very short, and hence the impulsive force very large, then the change of momentum due to all other external forces to the two body system (e.g. gravity etc.) may be neglected. Hence, form the Principle of Conservation of Momentum, the total momentum of the system remains constant during the impact and is therefore the same after the collision as before it. Initial momentum Final momentum As momentum is conserved

The impulse may be found by considering any of the bodies. Impulse on body A

Impulse on body B

Note that the sum of the two impulses is ZERO! And that the impulse gained by one body equals the impulse lost by the other. The momentum principle gives us one equation relating the masses, initial and final velocities of the bodies. We usually know something about the initial velocities and masses (remember the mass remains constant!); in order to solve the equation we need to have some other information concerning the final velocities (i.e. we need to know something about either or ). One possibility is that there is NO REBOUND and the masses combine and travel on coupled together with a common velocity (i.e. ). One consequence of using the Principle of Conservation of Momentum is that although the momentum remains constant, the kinetic energy does not have to; if the collision was inelastic (with deformation taking place) then there will be a loss of kinetic energy from the initial to the final state.

Conservation of linear momentum

6

Foundation Mechanics

H10FM1

Laboratory 2

Results Part (a) Mass of vehicle =

kg

Length of mask =

cm

Running from left to right

First velocity

m/s

Second velocity

m/s

Difference in velocity

m/s

Fraction of momentum lost due to friction

Running from right to left

First velocity

m/s

Second velocity

m/s

Difference in velocity

m/s

Fraction of momentum lost due to friction

Questions to be answered from this first part of the experiment 1. 2. 3. 4. 5.

Is there any difference depending upon direction? What does this mean for the theory of Conservation of Momentum? Why are the velocities not the same? Where does the external force come from? Should this be allowed for in your next set of results? How?

Conservation of linear momentum

7

Foundation Mechanics

H10FM1

Laboratory 2

What to do There is a spreadsheet available for you to use to calculate the momentums and kinetic energies from your results. After you have taken the relevant results enter the results into the spreadsheet associated with this laboratory. Only enter data into the yellow cells and the spreadsheet will then calculate everything else. All the graphs should be automatically drawn for you. You will need to check the values calculated in the spreadsheet! Pick one set of results and go through the calculations, showing the detail in the report. For example, calculate the total momentum at each stage in one run and then determine the percentage change in momentum Percentage change in momentum The result form the spreadsheet, if you are happy with the way it calculates it, will enable you to gauge how much momentum has changed during the impact. Look at the graph of initial momentum against final momentum. Draw on the graph the ideal line (initial momentum equals the final momentum) so that you can see what you should obtain. Why are your results different to the ideal line? Next, look at the initial kinetic energy and the final kinetic energy for each trial. The change in kinetic energy that has occurred and the percentage change in kinetic energy will been determined by the spreadsheet. Again check the spreadsheet working. Percentage change in inetic energy Look at the graph of initial kinetic energy against the final kinetic energy. Draw on the graph the ideal line (initial kinetic energy equals the final kinetic energy) as well as the TRENDLINE for your results. Why are your results different to the ideal line? Look at the graphs and see if you can make any comments about the shapes. What do the two gradients of the lines represent? Should there be a gain of momentum or kinetic energy? Why not? Don’t forget to show one TYPICAL calculation of your results (i.e. take one set of results from one trial and show how each quantity such as momentum and kinetic energy has been calculated)

Conservation of linear momentum

8

Foundation Mechanics

H10FM1

Laboratory 2

Discussion and conclusions You should include, as a matter of course for any experimental write up, a discussion, where you discuss the experiment and include any material you have found from your research. The conclusions should simply be a series of statements that show what has been found out during the experiment; this should NOT include any discussion of the results (that’s what the discussion is for!) Some topics for discussion could include (although this list is by no means extensive i.e. you can feel free to add other topics) :a) From the calculations, what can you say about the theory of Conservation of Momentum? Is the theory correct? What affect does the nature of the collision have on the theory? b) Look at the change in kinetic energy for each run of the experiment. What does this tell you about the collisions? Is energy conserved? How? c) Are there any reasons why the results and theory do not agree? What about your findings from part (a)? How significant are they? If these are included, what could you deduce? d) What errors have been introduced into the experiment? How could they be reduced?

Conservation of linear momentum

9

Foundation Mechanics

H10FM1

Laboratory 2

Name : Student ID:

Date:

The following questions are to be answered and handed in at the end of your session in the laboratory on the reverse side of this sheet. (1)

Which of these statements best describes the difference between an inelastic collision and an elastic collision? Give reasons for your answer, explaining why the other statements are incorrect. (a) If colliding objects stick to each other after the collision, the collision is inelastic; otherwise, it is elastic. (b) If there is external force acting on the system, the collision is inelastic; otherwise, it is elastic. (c) The potential energy of the system is not conserved in an inelastic collision, but it is conserved in an elastic collision. (d) The kinetic energy of the system is not conserved in an inelastic collision, but it is conserved in an elastic collision. (e) The linear momentum of the system is not conserved in an inelastic collision, but it is conserved in an elastic collision.

(2)

Two vehicles with masses m and M sit on a frictionless air track. The cart with mass m is given an initial push towards cart M (which is at rest). If the collision of the vehicles is elastic and mass M is larger than mass m, then after the collision: (a) both vehicles will move in the same direction (b) the vehicles will move in opposite direction (c) the first cart will come to rest and the second cart will move with the same velocity as the first one. (d) both vehicles move with the same velocity which is half of the initial velocity of the cart with mass m. (e) none of the above

Conservation of linear momentum

10

Foundation Mechanics

Conservation of linear momentum

H10FM1

11

Laboratory 2

Foundation Mechanics

H10FM1

Laboratory 2

Results

Experiment b) Elastic collision between two vehicles, one initially at rest. Mass of moving vehicle

Mass of stationary vehicle

Initial velocity of moving vehicle

Final velocity of moving vehicle

Final velocity of initially stationary vehicle

m1 (kg)

m2 (kg)

U1 (m/s)

V1 (m/s)

V2 (m/s)

Conservation of linear momentum

12

Foundation Mechanics

H10FM1

Laboratory 2

Experiment c) Inelastic collision between two vehicles, one initially at rest. Mass of moving vehicle

Mass of stationary vehicle

Initial velocity of moving vehicle

Final velocity of both vehicles

m1 (kg)

m2 (kg)

U1 (m/s)

V (m/s)

Conservation of linear momentum

13