April 03, 2017 Lab 9: Centripetal Force with a Motor

Lab 9: Centripetal Force with a Motor

Chris Ceron, Amy Chung, John Choi

Goal of Lab

Use apparatus to establish a relationship between  and 

 

Apparatus and measurements used to establish the relationship between  and 

Theory/Introduction

We know there exists a relationship between centripetal force and angular speed ():

 = radius

 = angular speed

Through a free body diagram, we can establish a relationship of the different forces acting on our apparatus.

We called the height from the ground to the top of the string H, and the height from the ground to the mass h. Using this, we can find the vertical length of the string as it is rotating, and allows us to solve for .

                 

We can also derive for the angular speed using our sum of forces. We solved for T through the y-component of the forces and plugged it into T for the x-component:

r is the sum of the length of the top rod (R), and the x component of the string as it is rotating (Lsin). 

 

Procedure

Our apparatus is composed of a tripod with a vertical rod on top. Attached to the top of the rod is another rod attached horizontally. We attached a hanging mass to the end of the horizontal rod using a lightweight string. A motor attached to the tripod and rotates the rods and various speeds. 

We used our apparatus for five different cases, each case with a different speed. For each case we recorded the amount of time it takes for the hanging mass to rotate ten times. For each case we also record the height (h) between the ground and the hanging mass by using a stand with a piece of paper attached to it. We can adjust the height of the paper until the hanging mass makes contact, then record the height between the ground and the paper.

Data:

The height from the ground to the top rod (H), the length of the rod (R), and the length of the string (L) are all constant in each case.

Height	Length	Radius
1.82 ± 0.001 m	1.59 ± 0.001m	0.75 ± 0.001m

Data for our five trial runs:

	height (m)	time for 10 rev (s)
1	0.36± 0.001 m	33.41
2	0.655± 0.001 m	27.37
3	0.87± 0.001 m	24.22
4	1.132± 0.001 m	19.92
5	1.36± 0.001 m	15.65

Calculated Data

In this lab, we found  two ways. The first was mentioned in the theory/introduction section:



The second method used was to compare the time it took for one revolution:



2 = one revolution
T = time period to complete one revolution

	θ (degrees)	ω (using angle) (rad/s)	ω (using period) (rad/s)
1	23.3	1.749505216	1.880630143
2	42.9	2.229344963	2.295646806
3	53.3	2.548188044	2.594213587
4	64.4	3.060365349	3.154209492
5	73.1	3.768444183	4.014814893

We used both calculations of ω, plotted them on a graph, and applied a linear fit.

Conclusion:

The two ω calculated should be identical. As shown in the graph above, the slope of the graph is 1.045, which is reasonably close to our expected value of 1. The uncertainty value of our slope is +/- .01039 or 0.994%. Our biggest source of error was recording the amount of time it took the hanging mass to revolve ten times. We recorded this measurement by using an application on our phone and timing when the mass approximately revolves ten times. Overall, we received a high correlation between both ω calculated. We can conclude that there is a relationship between  and ω.