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Atwood's Machine

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Introduction

Atwood’s Machine                                Alex Chen

Aim and task:

2(m1+m2)h = (MA+B)t^2

Assuming that (m1 + m2) is constant, plot a graph from which the value of the constants A and B can be deduced. And find out what the values should be.

Method:

Set up a pulley with 2 masses, m1 and m2 suspended on either side by a strong thread/string so that m2 is about 1.5m off the ground when m1 is resting on it.

With m2 = 280g and m1 = 250g, obtain an accurate time for m2 to travel from rest through the distance ‘h’ to the ground.

To do this, hold on mass m2 and ready to time, let m2 fall freely, and start the timer the same time. Stop the timer when it hits the ground (book). It will produce a loud noise when it hit the book.

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Middle

Working formulas out:

2(m1+m2)h=(MA+B)t^2

kh = (MA+B)t^2

kh=Mat^2+Bt^2

kh-Bt^2=Mat^2

(kh-Bt^2)/M=At^2

(((kh-Bt^2)/M)^1/2)/t=A

(2k^2)/(t^2)=MA-B

((m1-m2)*g-Ff)t=(m1=m2)2h

Ff= frictional force  

Conclusion:

I have found out that A would be the gravity, and B would be the frictional force in this equation. And the value I have found is that A= 10, B=72 I was allowed 10% errors as I have explained in the evaluation below, and my only have very small errors since that I knew gravity should be about 9.8. My experiment was very well done.

Evaluations:

Over all I think my experiment went well, there were some errors, but they were good enough to prove my theory. The errors can all be explained. First there are some obvious errors, such as the errors coming from the weights.

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Conclusion

. So over all there is a total of 15% errors that I could have had.

...read more.

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