# Beagle 2 - landing on Mars: results

The traces below show the results obtained from the landing on Mars science experiment.

As can clearly be seen from the results, the trace produced by the model falling on carpet is quite high (large voltage = large force) as shown in Figure 4, but of short duration.

However, when the balloon is below the model the trace, as shown in Figure 5, is very low (low voltage = low force) but of long duration.

Figure 4: Trace without balloon attached

Figure 5: Trace with balloon attached

Q1. The force will be lower than without the balloon, but the time for which the force acts will be longer.

Q2. You would want a low output voltage (low force) in order to obtain a cushioned landing. Small forces on the spacecraft are likely to do far less damage to it and its scientific equipment. Small forces on impact also mean a much smaller deceleration, again lessening likely damage.

Q3. You would want a long impact time as this would lessen the deceleration.

Q4. With a smaller height of fall the spacecraft’s momentum on impact would be lessened so, on impact, if the impact time was roughly similar the impact force (output voltage) would be smaller (force = rate of change of momentum.) Alternatively, looking from the acceleration point of view, the spacecraft’s velocity would be lessened and so, if the impact time was roughly similar to that before, the change of velocity would be lessened, the deceleration lessened and the impact force lessened.

Q5. With a smaller mass the spacecraft's momentum on impact would be lessened so, on impact, if the impact time was roughly similar the impact force (output voltage) would be smaller (force = rate of change of momentum.) Alternatively, looking from the acceleration point of view, if the impact time was roughly similar to that before, but with the same change of velocity on impact, the deceleration will remain the same. However, with a smaller mass the impact force will have lessened.

## Teachers’ notes

This experiment is probably best conducted as a demonstration activity with pupil support. A large display screen would prove useful.

Pupils should note that the trace produce by the model falling on carpet is quite high (large voltage = large force) as shown in the results above, but of short duration. However, when the ballon is below the model the trace is very low (low voltage = low force) but of long duration.

Relate the traces, which are effectivley Force–Time graphs, to the change of momentum of the model and the impulse experienced on landing. If the model had exactly the same velocity (fell exactly through the same height) on impact each time then its change of momentum would be the same, so the impulse must be the same also. Since the impulse is the area under the Force–Time graph, then these areas should be the same. The areas could be measured by counting squares. Alternatively you could look at the balloon system as one which reduces the acceleration (negative in this case) and so the force of impact on landing, relating to the expression F=ma.

It is possible to calibrate the sensor in terms of the force on it and, with PicoScope, re–calibrate the voltage scale in terms of the force in Newtons. For the former it is simply a matter of resting a known mass (say 50 g) on the sensor button and noting the voltage, and doing likewise for 0g. The difference in voltage then represents the force due to a 50 g mass. Re–calibrating the scale is achieved through the Custom Range settings of PicoScope. As this is intended as a fairly quick demonstration, it is suggested that spending time doing this is not worthwhile for the vast majority. However, a very able pupil might be given such a task to tax their ingenuity.

The force sensor is based on piezoresistors which flex under an applied force, this changing their resistance in a Wheatstone bridge type circuit, and so the voltage across it. Further details on the force sensor can be found on its datasheet available online from Farnell InOne. As it is a fairly expensive sensor the apparatus design allows it to be removed from its socket housing and used elsewhere.

## Safety issues:

Ensure fingers are kept a safe distance from where the Beagle 2 model will "land" !

Target age groups:

Ages 14 + (Key Stage levels 4 and POST 16)

## National curriculum:

Double science Key Stage 4
Forces and motion
2 Pupils should be taught:
Force and acceleration
d) that acceleration is change of velocity per unit time
f) the quantitative relationship between force, mass and acceleration

Subject criteria for Physics at As/A2:

3.5.3 Dynamics: Use of F = ma in situations where mass is constant
3.6.1 Momentum concepts: Force as rate of change in momentum in situations where mass is constant

Unit 4 Controlling the Transfer of Energy

Getting moving and stopping

You need to be able to:

Use Newton’s second law in the form F = ma
Apply Ft = mv - mu to collision processes (in words, impulse = change of momentum)
Investigate how safety is enhanced, and damage limited, by:
— lengthening collision times
— reducing collision speed

## Technicians’ notes

Apparatus list

The items below are required for the construction of the Beagle 2 lander model:

• 1 force sensor FSG15N1A (Farnel InOne 721-6671)
• 1 force sensor mounting bracket (Farnel InOne 721-6683)
• Plastic downpipe (Marley 68 mm RPH252BX)
• Quickset cement
• 2 4 mm socket red (JPR 705-230)
• 2 4 mm socket black (JPR 705-231)
• 1 1N4001 diode (JPR 1N4001)
• 1 PP3 battery clip (JPR 440-006)
• 1 9 V PP3 alkaline battery*
• 1 4 mm plug red (JPR 706-197)
• 1 4 mm plug black (JPR 706-198)
• 1 socket housing 4-way (JPR 710-604)
• Crimp terminals (JPR 710-660)
• Thin connecting wire
• Small screw eye
• Small Plastiplug
• Terry clip to fit PP3 battery
• Dowelling to fit retort stand boss
• Thin wooden or plastic rod to anchor string
• Styrene sheet 2 mm * 10 cm * 10 cm (W Hobby or local model shop)
• string
• screws
• yellow paint

* A supply voltage of between 10 V dc and 12 V dc maximum is specified but a 9 V PP3 alkaline battery was found to work OK.

## Construction method

Saw off two lengths of plastic downpipe 2.5 cm and 3.5 cm in length to make the model moulds. Put a little oil or soap solution around the insides of the moulds. Place these in a tray, pour in quickset cement and leave to dry.

Figure 1: Beagle 2 model

Release the model from the moulds by sawing carefully through the plastic sides at one point. Drill holes in the cement cylinders as shown in Figure 1 and paint the cylinders yellow. Fit a small Plastiplug into the back/topside of each and fit a screw eye into these. Fit another small Plastiplug into the hole with which to attach the sensor mounting bracket, screw the bracket in place with the force sensor. Crimp four thin insulated leads of length 50 cm each to the crimp terminals and inset the latter into the socket housing. Pass the wires through the outer hole in the cement cylinder and through the screw eye. Push the socket housing onto the force sensor.

Figure 2: Sensor platform

Construct the sensor platform as shown in Figure 2 above and solder the leads to the appropriate sockets, incorporating a 1N4001 diode into the 9 V battery line with its band (cathode end) furthest from the red 4 mm socket. This diode will protect against reverse battery connections to the force sensor. Figure 3 below shows the connections to the force sensor.

Figure 3: Connections to the force sensor

Finally, tie a 40 cm length of string to the screw eyes and pass this through the platform’s central hole and tie to a thin plastic or wood rod to anchor it. Screw the Terry Clip in place on the underside of the platform. Connect a red and black 4 mm plug, as appropriate, to the PP3 battery clip.

UK suppliers

Farnell InOne
Leeds
LS12 2TU
Tel: 0870 1200 200
Web:www.farnell.com

W Hobby Limited
Knight’s Hill Square
London SE27 0HH
Tel: 020 8761 4244
Web: www.hobby.uk.com

JPR Electronics Ltd
Houghton Regis
Dunstable
Tel: 01582 470000
Web: www.jprelec.co.uk