By plotting the graphs it can be observed the y axis is equal to v” and the x axis is given as r (radius), the gradient is given by (y2 – y1) / (x2 – x1). By working out the gradients it can be seen that the gradient for 50-gram masses is approximately 26, whilst the gradient for the 100-gram graph is approximately 53.27, approximately double the gradient of the 50-gram graph. It can also be observed the any two points taken for the 50 gram graph will have a relatively close gradient to any other two points, hence the graph has an almost constant gradient. The significance of all this will be discussed in the questions.
1 What is the relationship that these graphs indicate?
The graphs show that v”is proportional to radius as straight lines with constant gradients were achieved when drawing the graphs of v”/r (as explained before). This phenomenon is a result of the gradient being equal to mg/M, as v” = r mg/M, in our experiment all these mass factors were controlled and kept constant ie 18.49 gram bung was used and 50 or 100 gram mass was used as needed, also gravity was constant so mg/M was constant and so was the gradient. Hence mg/M is a constant and v (orbital velocity) is directly proportional to r (radius of orbit).
Furthermore when the graphs were drawn it was seen that when that when the mass carriers were doubled form 50 to 100 grams the gradient also doubled. It was concluded that this was because the gradient was given by mg/M. Therefore when m was doubled the gradient doubled. This showed that if the mass of the object in orbit or mass of central object changed so too would v”/r.
2 what does the slope of your v” versus r graph represent?
Because v” = r mg/M it was believed the gradient of the graph represented mg/M. proof of this is the graphs show that v”is proportional to radius as straight lines were achieved when drawing the graphs of v” verus r, mg/M is also a constant value and this correlates with the constant slope achieved. Thus drawing the graphs and achieving a constant gradient for each mass supported this idea. When mass was doubled the gradient was also doubled this also shows gradient is equal to Mg/m where when m (mass carrier) is doubled whole gradient doubles showing velocity increases as mass increases.
3 what role does gravity play in the results in this experiment?
In this experiment gravity along with the masses provide the centripetal force, which holds the rubber stopper at a particular radius. The acceleration factor of the force(ma)
Is given by the acceleration of gravity. Therefore when the mass is 100 grams the centripetal force is given by 0.1x 9.8= 0.98 N. The centripetal force must be equal to the gravitational force in order to hold the rubber stopper at a constant radius. Where Mv”/r = mg.
The gradient of the 100-gram graph was not precisely double the gradient of the 50-gram graph. This can be attributed to simple human errors while calculating results. Despite all this the shape of the graph was still as hypothesised because a line of best fit was taken. Human errors include slight discrepancies in maintaining a constant orbital velocity, Furthermore, when measuring the radius of orbit, the angle during which the bung was spun was estimated and this may have also been a source of error. Also whilst spinning the bung unintentional fidgeting of the hand was encountered consequently altering the orbital velocity. Furthermore improvements to the original method were made by measuring the time taken for twenty oscillations rather than ten in this manner any time measuring error would be minimised.
The factors affecting some of the objects undergoing uniform circular motion were examined. The quantitative relationship between the variables of force, velocity and radius were determined. It was found that velocity is directly proportional to radius as v”/r when plotted gave a straight line with mg/M as gradient. The gradient for the 50-gram graph was found to be approx 26 and gradient of the 100-gram graph was found to be double approx 53. slight discrepancies were found and these were attributed to human errors such as measuring. However the effects of these errors were minimised by taking a line of best fit eventually giving a straight-line graph representing v” is proportional to r.
Jacaranda HSC Science PHYSICS 2 Michael Andriessen, Peter Pentland
PUBLISHED 2003 BY JOHN WILEY AND SONS AUSTRALIA.