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Model the motion of a trolley running down a slope.

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Introduction

Halley Porkess        Mechanics 2 Coursework        09/05/2007

Investigation- modelling the motion of a trolley running down a slope

Aim

To model the motion of a trolley running down a slope.

Procedure

  1. Set up apparatus as shown in diagram above.
  2. Measure vertical height of stand, measure distance from base of stand to where the ramp meets the desk. Measure length of piece of card on the trolley, this is x. Also record the mass of the trolley.
  3. Mark on the ramp distances of 0.1m, 0.3m, 0.5m, 0.7m, 0.9m, 1.1m, 1.3m, 1.5m, and 1.7m up the ramp from the light gate.
  4. Place the front of the trolley on the 0.1m mark, reset the millisecond counter, and release the trolley.
  5. Repeat step 4 twice.
  6. Repeat steps 4 and 5 for distances of 0.3m, 0.5m, 0.7m, 0.9m, 1.1m, 1.3m, 1.5m, and 1.7m.

Experimental results

Mass of trolley is 1031g

Horizontal length of ramp is 2.315m

Vertical height of ramp is 0.11m        

Length of piece of card on trolley, x is 0.25m        

Ramp distance, s (m)

Reading 1 (s)

Reading 2 (s)

Reading 3 (s)

Average reading, T (s)

0.1

0.756

0.761

0.748

0.755

0.3

0.510

0.496

0.523

0.510

0.5

0.406

0.414

0.410

0.410

0.7

0.339

0.341

0.347

0.342

0.9

0.292

0.295

0.293

0.293

1.1

0.260

0.260

0.260

0.260

1.3

0.235

0.234

0.235

0.235

1.5

0.215

0.216

0.216

0.216

1.7

0.213

0.212

0.212

0.212

...read more.

Middle

opposite/ adjacent. Therefore, image03.png

The table below compares theoretical timings against the real times, using the formula image04.png

Ramp distance, s (m)

Theoretical time, t (s)

Experimental time, T (s)

0.1

0.546

0.755

0.3

0.397

0.510

0.5

0.328

0.410

0.7

0.285

0.342

0.9

0.256

0.293

1.1

0.234

0.260

1.3

0.217

0.235

1.5

0.203

0.216

1.7

0.192

0.212

The theoretical times are all lower then the experimental times, which indicates that there is something wrong with the modelling. To check this, I am going to work backwards to obtain a value for g.

As image05.png , image06.png, therefore image07.png

s (m)

t (s)

g (ms-2)

0.1

0.755

5.134

0.3

0.510

5.956

0.5

0.410

6.267

0.7

0.342

6.823

0.9

0.293

7.482

1.1

0.260

7.951

1.3

0.235

8.367

1.5

0.216

8.684

1.7

0.212

8.027

These values of g are appear to have a trend- however, I am now going to work out the error bounds for g, using the error bounds for t, found earlier.

G is tending to something slightly above 8, as Graph 1 shows. So even if it reaches 8.5 this is an error of nearly 15% on its true value of 9.81. My estimate of experimental errors are as follows:

Timing: accurate, no error (done electronically)

Measurement of

...read more.

Conclusion

F is image17.png.

s (m)

Ek observed (J)

EP lost (J)

Work done against friction (J)

Frictional force, F (N)

0.1

0.0565

0.1080

0.0515

0.2289

0.3

0.1239

0.2040

0.0801

0.1885

0.5

0.1917

0.3000

0.1083

0.1733

0.7

0.2755

0.3960

0.1205

0.1461

0.9

0.3753

0.4920

0.1167

0.1139

1.1

0.4766

0.5881

0.1115

0.0910

1.3

0.5834

0.6841

0.1007

0.0707

1.5

0.6906

0.7801

0.0895

0.0551

1.7

0.7169

0.8761

0.1592

0.0872

An average value for the frictional force F, is 0.1283

Conclusion

The original model of ignoring friction was not satisfactory. There clearly is resistance, as shown above. The resistance is not constant, however it seems to be greater at low speeds. A revised model could include a resistance force of 0.1N. This would be better but still not particularly accurate.

Further investigation would be needed to give more information about the frictional force. A better method would be to release the trolley with a electromagnet, which starts one millisecond timer, and allow the light gate to stop one millisecond timer, but start another, as in the experiment. This would mean that the error in releasing the trolley is less, and constant, and that there are two times, so there are actually two sets of data that can be compared against the results.

...read more.

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