# Investigating circular motion

AIM

To examine some of the factors affecting the motion of an object undergoing uniform circular motion, and then to determine the quantitative relationship between the variables of force, velocity and radius.

APPARATUS

Rubber bung Metre rule 50 gram slot masses

Glass tube 50-gram mass carrier 50-gram slot masses Metre rule

Stopwatch Sticky tape Metre rule String

THEORY

As in Jacaranda HSC Science Physics 2 p.54

In this experiment when the rubber bung is moving in a circular motion and the string it is tied to moves neither up or down a constant radius is being maintained. For this to be true the centripetal force must equal the gravitational force hence

Mv"/r = mg from this

v"/r =mg/M and v" ∞ r therefore as v increases so does r and vice versa.

Where

m = Mass of mass carrier + masses (kg)

g = acceleration due to gravity 9.8 m/sec"

M = mass of object in motion (kg)

v = instantaneous velocity of mass (m/sec)

r = radius of circular motion (m)

METHOD

As in Jacaranda HSC Science Physics 2 p.54

However instead of measuring the time for 10 revolutions, the time for 20 revolutions was measured, this allowed more accurate results to be obtained. Furthermore the lengths given in the book were used as merely guidelines and not followed precisely also 50 and 100-gram masses were used.

RESULTS

Force (N) Radius(m) Period (20 Revolutions) (s) Orbital Velocity v m/s v"

g x 50g 1.03 19.47 6.65 44.19

g x 50g 0.83 17.02 6.12 37.55

g x 50g 0.64 14.14 5.68 32.35

g x 50g 0.37 9.94 5.2 27.04

g x 100g 1.06 16.86 7.9 62.41

g x 100g 0.82 14.4 7.15 48.702

g x 100g 0.62 12.8 6.08 37.01

g x 100g 0.44 10.2 5.42 29.38

Results of circular motion experiment

Velocity" versus r

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.

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...

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