## DrDAQ

#### Data logger, oscilloscope, signal generator and more!

DrDAQ is a versatile instrument that connects to the USB port of any PC. Using the supplied PicoScope software it can be used as an oscilloscope, spectrum analyzer and signal generator.

# Runaway train science experiment - results

The trace shown in Figure A36.3 shows the result of a collision with a buffer packed with foam sponge.

Figure A36.3 Trace produced by collision with a foam sponge buffer

After the collision record the final voltmeter reading Vt and obtain a print-out on graph paper of the screen trace. Ensure that you note the details of both the voltage and time axes’ scales if they are not automatically printed. Repeat as required.

## Analysis of results

Part 1: In general, for an impact to be least dangerous to passengers or damaging to the materials being transported, the force (voltage) - time trace for the collision should be as long (in time) and as small in amplitude as possible. Compare the traces for different buffer designs to see who has the best energy absorbing structure.

Part 2: Use the two voltmeter readings Vo and Vt, the distance travelled by the wagon whilst the capacitor was discharging, and the value RC of the resistor-capacitor combination in the timing circuit, to calculate how long the discharge lasted, and so the time of travel of the wagon whilst this occurred. Noting that the collision with the sensor occurs after this time, calculate the velocity with which the wagon hit the buffer and its momentum. (Assume uniform acceleration down the slope.) See Additional Sheet section 2 if you need help with this.

Use the Voltage - time trace, the value of the force which produces a voltage output of 100 mV, and the value of the wagon’s momentum before the collision with the buffer, to calculate the velocity with which it bounces back off the buffer. See Additional Notes if you need help with this.

## Section 1: Using the data from the calibration of force sensor

Weight of box with sand = 100 gf = 0.1 kgf = 0.1 kg 9.8 N kg-1 = 0.98 N
So a force of 0.98 N produces a voltage output of Vload - Vno load = 21 mV.
Therefore 0.98 X (100/21) N , or 4.67 N, produces a voltage output of 100 mV.

## Section 2: Finding the velocity of the wagon as it collides with the buffer

V0 = 6.08 V
Vt = 5.49 V average
RC = 10.0 s

So taking Vt = V0 x e-t/RC , where t is the time of discharge, we have, taking logs to the base e:
loge Vt = loge V0 - t/RC. loge e

Giving loge 5.49 = loge 6.08 - (t/10) x 1
So 1.703 = 1.805 - t/10 and so t = 1.02 s

The distance of travel down the runway whilst the capacitor was discharging was 0.79 m so, using s = ut + ½at2, we have:

0.79 = 0 + (0.5 x a x 1.022) and so a = 1.52 m·s-2

So the velocity on collision with the buffer is given by v = u + at where v = 0 + 1.52 m·s-2 x 1.02 s = 1.55 m·s-1.

Therefore the momentum of the wagon on collision was 0.187 kg x 1.55 m·s-1 or 0.290 kg m·s-1.

## Section 3: Finding the change of momentum on collision

The impulse, and so the total change of momentum that took place, is shown by the area under the Voltage (force) - time trace above the baseline voltage. Calculate this first in terms of the number of small squares occupied. On that shown by area A in Figure 36.3 (figure above) the number of squares was 459.

Now to calculate how large an impulse or change of momentum each square represents. Count the number of squares on the graph paper in the area marked B (150 to 250 mV) x (-20 to 0 ms). In Figure 36.4 it is 145. 100 mV represented a force of 4.67 N, so this number of squares represents an impulse or change of momentum of (4.67 N x 20 ms) or 0.0930 Ns or 0.0930 kg m·s-1. So each square represents 0.0930 kg m·s-1/145 or 0.000641 kg·m·s-1 and the area of the trace (0.000641 kg ms-1 459) or 0.294 kg ms-1.

Now to calculate how large an impulse or change of momentum each square represents. Count the number of squares on the graph paper in the area marked B (150 to 250 mV) X (-20 to 0 ms). In Figure 36.4 it is 145. 100 mV represented a force of 4.67 N, so this number of squares represents an impulse or change of momentum of (4.67 N x 20 ms) or 0.0930 N·s or 0.0930 kg·ms-1. So each square represents 0.0930 kg·ms-1/145 or 0.000641 kg·m·s-1 and the area of the trace (0.000641 kg·m·s-1 459) or 0.294 kg·m·s-1.

Figure T36.1: wagon

## Finding the velocity with which the wagon bounces back off the buffer

The change of momentum indicated by the area of the trace will be equal to the sum of the momentum of the wagon as it collides with the buffer and of the wagon as it bounces back off the buffer.

The wagon’s momentum as it collided with the buffer was 0.290 kg·m·s-1, so its momentum on bouncing off must have been (0.294 - 0.290) kg·m·s-1 or 0.004 kg·m·s-1. With the wagon having a mass of 0.187 kg this gives a bouncing back velocity of 0.004 kg·m·s-1/0.187 kg = 0.021 m·s-1.

## Teachers’ notes

This final activity of the A2 unit Transport on Track brings into play a number of facets of physics dealt with in the unit: knowledge of (i) how the time-constant RC affects a rate of discharge of a capacitor and the voltage across it, (ii) how to calculate (with uniform acceleration) acceleration and velocity when a time and distance of travel are known and (iii) how to calculate the momentum change from the area under a Force-time graph.

The activity has been split into two parts. Initially the students select the material which they feel will provide the safest bumper to bring the wagon to rest. Print-outs obtained of the Voltage (force) - time graphs can be compared and that with the lowest voltage (force) for the longest time would be the winner.

In the second part, possibly done for homework, the students can use the rest of the data collected, and their collision graph, to calculate the velocity with which the wagon rebounds from their buffer. This gives practice at calculating areas under graphs, using information to calibrate a sensor, using the expression

Vt = Vo.e-t/RC, and using equations of motion.

Using Pico DrDAQ or ADC-40/42 with PicoScope software, useful results were obtained with the timebase set at 20 ms/div; the trigger at single, trigger level rising and at about 20 mV*; the X-gain at 1; the Y-gain at 20; and the % advance at -10%. With the trigger setting on ‘single’ the trace obtained remains on screen. Traces can be saved then or, with ‘autosave’, saved automatically.

The force sensor is a piezo-resistive device and is linear in response up to near 15 N. Any off-centre collision with the plunger has minimal effect, although it is best to arrange for the buffer box to be positioned as centrally as possible.

* You may be able to lower this value but it must be high enough to prevent triggering too early.

## Technicians’ notes

### Apparatus

• Wagon (see construction details)
• Sloping track (see construction details)
• Force sensor (see construction details)
• RC timing unit (see construction details)
• Voltmeter 0 - 10 V f.s.d.
• BNC plug to 4 mm plugs (for ADC-40/42 only) Pico part no MI029
• PC running PicoScope
• 6 V battery
• 4 mm stackable plug red JPR 705-285 (For DrDAQ only)
• 4 mm stackable plug black JPR 705-286 (For DrDAQ only)
• Extra flexible connecting wire red JPR 780-080 (For DrDAQ only)
• Extra flexible connecting wire black JPR 780-081 (For DrDAQ only)
• Paving bricks (3) or lab-jack to raise level of one end of runway
• Various materials for making buffers - sponge, tissue paper, Oasis foam, kitchen towel, cardboard, aluminium foil, paper straws, plastic bags, balloons, Blu-Tack, Soft Stuff (toy shop), Plasticine
• Potting box (Medium size) Maplin FD97
• Felt-tip pen
• Meter rule
• Emery cloth
• Sellotape (Scotch tape)
• Scissors

*For DrDAQ connection is made via V and Gnd and it is recommended that you screw a red lead terminated by a 4 mm plug into V and a black lead terminated by a 4 mm plug into Gnd.

### For making the wagon

Meccano parts:

• Flanged plate 11 holes 5 holes (1) Frizinghall MO52
• Trunnion (5) Frizinghall M126
• Flanged wheel (4) Frizinghall MO20
• Axle 200 mm length (saw into two) Frizinghall MO13A/R
• Spring clip metal (4) Frizinghall MO35
• Bolt 6 mm cheesehead zinc (6) Frizinghall MO37B/CZ
• Nut hexagonal zinc (6) Frizinghall MO37C
• Grub screw 4 mm slotted (4) Frizinghall MO69A
• Wooden drawer knob e.g. B and Q Sml Mush Knob RD509

The contact surface between the wagon’s wheels and the track will need to be cleaned with emery cloth before use. It is also wise to clean the axle rods where the grub screws of the wheels make contact.

Figure T36.2: sloping track

## For making the sloping track

• Chipboard shelf 150 mm x 1.5 m DIY
• Wooden battening 25 mm x 25 mm x 150 mm DIY
• Aluminum corner 15 mm x 15 mm x 1 mm x 1 m (2) B and Q
• Chipboard screws (6)
• Countersunk head screws 1.5 (2)
• 4 mm socket white (2) JPR 705-210
• Bolt (2)
• Nut (2)
• Solder tag (2)
• Connecting wire
• PVC tape
• Emery cloth

The aluminium corner is anodized and so has a non conductive coating all along it. This needs to be removed where indicated on Figure T36.2 and at the points where the nut, bolt and solder are attached. Use emery cloth to remove the coating. Place PVC tape over the aluminium where it is to remain insulated.

## For making the force sensor

• Paving brick
• Plastic downpipe 15 cm DIY
• Honeywell force sensor FSG15N1A Farnell 721-6671
• Force sensor mounting bracket Farnell 721-6683
• 4 mm socket red JPR 705-210
• 4 mm socket black JPR 705-206
• Battery clip PP3 type Maplin HF28F
• 9V PP3 alkaline battery
• Socket housing PCB latch Hseng 4-way Maplin HB58N
• PCB terminal Maplin YW25C
• Nut
• Bolt
• Washers (2)
• Connecting wire
• Cheesehead wood screw 1" (2)
• Plastiplug or similar (2)

Screw the plastic downpipe firmly to the brick using the screws and Plastiplugs. Bolt the force sensor in its clip centrally (vertically and horizontally) to the flat front surface of the downpipe. Do, however, ensure that a hole is made in the downpipe to allow venting of the force sensor - note a vent hole in its base.

Mount the two 4 mm sockets on the top surface of the downpipe.

Detach four terminal pins from the PCB terminal strip. Solder the battery clip to two of these. Solder wires to a further two terminal pins and then connect these to the red and black sockets on the downpipe respectively. Now push the PCB terminal strip pins into the socket housing so that, when it is pushed onto the force sensor the connections match with those shown in Figure T36.3.

Figure T36.3: connections to force sensor

## For making RC timing unit

Figure T36.4: RC timing unit

• Square section plastic downpipe (sawn in half) DIY
• Capacitor 10000 mF 16 V Maplin AU13P*
• 2.2 k vertical enclosed carbon preset UH14Q Maplin
• Switch SPDT toggle JPR 800-352
• 4 mm socket white (2) JPR 800-352
• 4 mm socket red (2) JPR 705-210
• 4 mm socket black (2) JPR 705-206
• Connecting wire

*The capacitor must be low leakage.

Adjust the value of the 2.2 kΩ pre-set resistor so that its combination with the 10000 mF capacitor gives a time-constant RC of 10.0 s. This is most easily achieved by connecting the RC timing unit up as shown in Figure T36.5.

Figure T36.5: RC timer unit set up for adjustment

Put the switch to ON to charge up the capacitor and note the reading on the voltmeter. Put the switch to OFF. Now place a shorting lead between the two white sockets, time for 10.0 s, and remove the shorting lead. The reading on the voltmeter now needs to be 0.37 (1/e) of what it was initially. Repeat, adjusting the preset resistor until this is the case.

If the voltage at the end of the time is too high, reduce the preset's resistance and vice versa.

NOTE: For near perfection one should include the wagon and the track’s contact resistance in this circuit when adjusting the RC timer unit to give a value of RC at 10.0 s. In reality their resistances are low, a few tens of ohms, and indeed do vary over the course of the run. Hence it is suggested that this refinement is ignored.

## Suppliers

Farnell
Leeds
LS12 2TU
UK

Tel: 0113 263 6311
Fax: 0113 263 3411
Web: www.farnell.com

Frizinghall Models and Railways
Frizinghall
BD9 4JZ
UK

Tel: 01274 542515
Fax: 01274 498281

JPR Electronics Ltd
Unit M
Kingsway Industrial Estate
Luton
Bedfordshire
LU1 1LP
UK

Tel: 01582 410055
Fax: 01582 458674
Web: www.jprelec.co.uk

Maplin Electronics
Freepost smu 94
PO Box 777
Rayleigh
Essex
SS6 8LU
UK

Tel: 0870 264 6000
Fax: 0870 264 6001
Web: www.maplin.co.uk

## Testimonials

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