Physics 20IB: Horizontal Circular Motion Lab

Aim: Determine the mass of a metal mass using the principles of horizontal circular motion.

Experimental Design:  A stopper that is attached to a vertical mass will be swung in horizontal circular motion using a specially set up apparatus. The purpose of the experiment is to find the experimental value of the vertical mass and compare in comparison with its actual value. (See diagram for more details)

Materials:

Procedure:

Find the mass of the rubber stopper and vertical mass to the nearest hundredth gram, record on data table.

Use a red marker and color a portion of the string, ideally somewhere in-between the upper clip and the glass tube on the bottom of the apparatus (ideal radius is 50cm-100cm), then a clip will be clipped around the red mark. This step will reduce errors when measuring the radius of the string after before each trial, and it will also ensure the radius stays constant on the apparatus throughout the experiment.

Measure the radius (measure before every trial) of the apparatus to the hundredth digit by using a meter stick, record the radius. The lab is now setup; we can now perform the experiment.

51.5

9

10

3.64

51.5

10

10

3.34

51.5

11

10

3.54

51.5

Average:

10

3.50

52.0

Miscellaneous Info:

Mass of Vertical Mass: 295.05g ±0.01g

Mass of Rubber Stopper: 19.45g ±0.01g

There are two main parts for the calculation of the vertical mass in this experiment; the first part of the calculations involves the horizontal swinging motion of the rubber stopper, which causes a centripetal force and tension on the string, the tension on the rope can be represented by the Fnet equation: Fc = T where T is the tension of the string

Therefore we can derive:

Since we have Number of Revolution, Time Required, and the Radius, we can calculate the velocity of the rubber stopper by using the equation:

 where t represents the period of the rubber stopper.

Average Number of Revolutions: 10

Average Time Required =

= 3.50 ±0.25s

Average Radius Length =

= 52.0 ±0.05cm

Propagation of Uncertainties:

Mass of Vertical Mass:

 (Uncertainty very small for mass)

Mass of Rubber Stopper:

 (Uncertainty very small for mass)

Measurement of Radius:

 (Uncertainty fairly small for radius)

Time Required Uncertainty: Since it is impossible for the naked eye to observe and record the time of exactly 10 rotations completed by the swung rubber stopper, therefore the uncertainty for the timing will be fairly large as it will account for both the counting and reaction errors. ±0.25s for the timing uncertainty should be a fair assumption.  Then,

Calculations for Tension of String:

Since v is unknown, we must calculate it, and then we can substitute its value in the centripetal force formula

Improvements:

The use of a more precise stop watch would be a valuable tool, because the stopper travels at a very fast speed, as the data processing shows, one revolution of the stopper takes an average of 0.35 second, the time relates directly to the speed (v) of the stopper, and this would ultimately affect the result on the centripetal force and the experimental result of the mass, therefore determining the period of the stopper as accurate as possible is crucial for the accuracy of the experiment. Secondly, the manual control of the swing has caused chaos in terms of systematic errors the experiment, to solve this problem realistically; we could use something similar to the mechanism of a pedal system on a bike, we can place it sideways and attach the glass tube onto one of the pedals and spin the other manually by hand, this could reduce the x direction made by the stopper to a minimum in the most affordable way, and would give us a better result. To reduce the twirl and friction of the string, we could use a softer string with fewer threads bind together; the softness of the string will reduce the friction to a minimum, with fewer threads bind together in the string, the twirl will be reduced to a minimum, lowering the systematic errors. All of the improvements about relates to the systematic errors as the percent error is larger compared to the percent uncertainty, they will reduce the systematic errors to a maximum and ensure better results.