Lab 9 Centripetal force with a motor

The purpose of this laboratory is to come up with a relationship between omega (w) and theta which is the angle that the string makes in the following diagram between L and the vertical.

The apparatus we used is an electric motor mounted on a tripod. A long shaft is connected to the motor . At the end of the shaft a horizontal rod is connected to it. At the end of the horizontal rod there is a long string of length L. Attached to the end of the string there is a rubber stopper. to measure height each we used a ring stand with a horizontal piece of paper sticking out of it.

The purpose of this instrument is to be able to use it to collect data for the period to find omega for different speeds of the motor. And to see the relationship that omega has on the size of the angle.

The first thing we did for this experiment was measure the H, R, and L. These measurements were H= 2 m, L= 1.645 m, R= .98 m.

We collected data for h and the time of ten revolutions for a certain speed:

Trial 1:
h = .455 m
t10 = 39.55 sec

Trial 2:
h= .578 m
t10= 34.6 sec

Trial 3:
h= .832 m
t10= 28.8 sec

Trial 4:
h= 1.025 m
t10 = 25.6 sec

Trial 5
h= 1.26 m
t10 = 21.4 sec

Trial 6
h= 1.485 m
t10= 17.5 sec

Next we had to find a relationship between theta and omega to do so we created a free body diagram to find the net force equations.

Although we have found a relationship between theta and omega we do not know what theta is so we are going to find out what we use to plug into theta with the given data that we measured.

we can use the following diagram of part of the apparatus to find out what theta is using trigonometry.

We know the measured length of L, and we can find one of the sides of the right triangle by subtracting the height of h that we measured with the height of H that was also measured. Knowing this we can derive an equation for theta as follows :

Plugging theta into the first equation we found and simplifying gives us the following expression:

Another way to find omega is by using the period T using the following expression:

Using these to equations we plugged them into logger pro and created a graph out of them the y axis was omega using the measurement of the height h. And the x axis was the omega found by using the period.

The graph tells us that the relationship that we derived for theta and omega is a good model . This is because our graph was a fairly straight line with a slope that is really close to one. The slope being close to one says that you get the same values using either equation to find omega. But like always our model is not perfect because there is a little bit of error that could have came from the fact that we had to guess when the weight at the end of the string actually crossed the paper on the ring stand so that we could start the time. Also taking the time for only ten revolutions is a small amount. To get a more accurate measure for the period it would have been better to take the time of 100 revolutions.