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

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**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:**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*?
## 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
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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