Part 1: 1. What is providing the centripetal force in Part 1? 2. How should the slope relate to the values of the mass of the rotating object, m and the radius of the circular path, r? I
Part 1: 1. What is providing the centripetal force in Part 1? 2. How should the slope relate to the values of the mass of the rotating object, m and the radius of the circular path, r? I
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter13: Gravitation
Section: Chapter Questions
Problem 44P: The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the...
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Transcribed Image Text:**Part 1:**
1. What is providing the centripetal force in Part 1?
2. How should the slope relate to the values of the mass of the rotating object, *m*, and the radius of the circular path, *r*?

Transcribed Image Text:## Circular Force Lab
### Part 1: Dependence of the Centripetal Force (F<sub>c</sub>) on the Speed of Rotation (V) at a Constant Radius
**Experiment Details: Vary V**
This table represents data collected to understand how the centripetal force changes with variations in rotational speed while keeping the radius constant.
#### Table 1
| Random Speed # | Time for 5 cycles (s) | Period, T (s) | ω (rad/s) | Random Speed v (m/s) | F<sub>c</sub> (N) |
|----------------|-----------------------|---------------|-----------|----------------------|------------------|
| 1 | 9.60 | 1.92 | 3.27 | 4.91 | 23.4 |
| 2 | 7.74 | 1.55 | 4.05 | 6.08 | 38.4 |
| 3 | 5.64 | 1.13 | 5.55 | 1.55 | 19.4 |
| 4 | 6.64 | 1.33 | 4.72 | 7.08 | 53.4 |
| 5 | 7.54 | 1.51 | 4.16 | 6.24 | 42.8 |
| 6 | 10.7 | 2.14 | 2.93 | 4.40 | 20.9 |
#### Calculations and Observations
- **Centripetal Force Equation:**
F<sub>c</sub> = m(v²/r)
- **Slope of F<sub>c</sub> versus v² (with units):**
0.766 kg/m
- **Expected Slope (in algebraic form):**
m/r
- **Numerical, Expected Value of Slope:**
0.712 kg/m
- **Percentage Difference Between Expected and Measured Slope Values:**
7.59%
### Explanation
1. **Time for 5 cycles (s):** The time taken for 5 complete revolutions.
2. **Period, T
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A tension force is also acting on rotating mass which provides centripetal force.
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