1 April 2015. Centripetal Force with a Motor

Purpose

1. to find a relationship between the angular speed and the angle formed by the apparatus described in the picture below (figure 1 section apparatus).
2. to use the model found (from number 1) to find several values of the angular speed in different specified conditions.
3. to measure the period (of the system) and calculating it with other known condition to find the angular speed from the same "different specified conditions".
4. to compare both the experimental values found from method 2 and 3, then finding the percent difference.

Apparatus:

The system. Designed to be exactly as the picture below, this system will enable us to do the action of circular motion in varieties of speed, which will resulted in difference of angle and height.

The left one is the real one. Right is the sketch (description below).

Description of the system.

• An electric motor mounted on a surveying tripod.
• A long shaft going vertically up from the shaft.
• A horizontal rod mounted on the vertical rod.
• A long string tied to the end of the horizontal rod.
• A rubber stopper at the end of the string.
• A ring stand with a horizontal piece of paper or tape sticking out.

Procedure:

1. The professor will first do a mock-up trial to show the student how does the system work.

Method 1 (ω_H omega w/height): using the model found to measure the angular speed

1. Then, we are given chance to measure all needed quantities to find the relationship between the angular speed and the angle (see picture)
2. From the result of the mock-up trial, we will calculate the angular speed from the model we found and see if it makes sense (more or less a match).
3. Then, the professor will increase the speed of the motor, resulting in a wider angle, and higher height, which is measured by the ring stand.
4. He will do this six times, thus we have six recorded values of height.
5. Then from these height, using the model, we will find omega (ω_H)

   

   Different speed of the motor, resulting in different angle, and different height

Method 2 (ω_T omega w/period) : measuring the period of circular motion to measure angular speed

1. In each height, we will also measured the period of this circular motion.
2. Then from the period we will also be able to find the omega (ω_T)

Data Analysis:

• Below is how we find the relationship between the angular speed and the angle with all the known quantities. Then we input the first data from the mock-up test and find that with h1=1.163 m, we find the omega to be 2.64 rad/s (0.420 rotation/s), which makes sense.

• Next, we use the next six height and input it into the model, and find omegaHeight.

SAMPLE CALCULATION. omega from trial 1, 2, and 3

omega from trial 4, 5, and 6

• Then, from the period we measure, we also find omegaT.

• We plot omegaT and omega Height to find the accuracy between these values. If the slope is sufficiently close to 1, then the error we make is smaller and vice versa. This is the graph of ω_T vs ω_H.

with slope 0.97

• Now, we find the range of error by analyzing the model that we got. Since both of the angular speed that we got are all experimental values, we are going to "guess" the percent error.
• From the picture, we analyze that the most uncertainties that we got is from the period and the measurement of the height. The rest we ignored.
• Then, we decide that the period have +/- 1% error.
• For the height in trial 1, we plug in the highest height (0.478 m) and the lowest height (0.468 m) to the model.

• Then we measure the percent difference of this calculation. (picture below)
• Now, we got the percent error!

• Now, we do this with every different height from every different trial, then calculate the average of all the percent error, then we get our final percent error.

Conclusions:

• In this experiment, we manage to find a relationship between the relationship between the angular speed and the angle of the system.
• From this relationship, we know that mass have no effect at all (quite surprising).
• Then, we compare the value we got from the relationship to the value we got from measuring the period of the system (the old-fashioned way) with percent error of 2.191 %.
• This error is, as calculated, from the uncertainties in measuring height and period.