Questions: Position three pulleys at the angles assigned for F1, F2 and the equilibrant force FE, exp = -FR of 3 and recorded in Table 1, and attach the masses corresponding to these forces to the ends of the strings passing over these pulleys. Add the force, F3, to the proper position and record its magnitude and position in Table 9. Determine the uncertainties δm and δθ by making an adjustment to the mass and the angle, respectively, until the ring shifts, but doesn't touch the pin, then calculate the uncertainty δF by using Eq. (5) and record all these values in Table 9. Write your result in the box below in the form F3 ± δF (in N) at θ3 ± δθ (in degrees) Compare the experimental and theoretical values for the F3 clearly stating the quantitative value you are comparing.

Position three pulleys at the angles assigned for F1, F2 and the equilibrant force FE, exp = -FR of 3 and recorded in Table 1, and attach the masses corresponding to these forces to the ends of the strings passing over these pulleys.
Add the force, F3, to the proper position and record its magnitude and position in Table 9.
Determine the uncertainties δm and δθ by making an adjustment to the mass and the angle, respectively, until the ring shifts, but doesn't touch the pin, then calculate the uncertainty δF by using Eq. (5) and record all these values in Table 9.
Write your result in the box below in the form F3 ± δF (in N) at θ3 ± δθ (in degrees)
Compare the experimental and theoretical values for the F3 clearly stating the quantitative value you are comparing.
Transcript text: Position three pulleys at the angles assigned for $\vec{F}_{1}, \vec{F}_{2}$ and the equilibrant force $\vec{F}_{E, \exp }=-\vec{F}_{R o f 3}$ and recorded in Table 1, and attach the masses corresponding to these forces to the ends of the strings passing over these pulleys. Add the force, $\vec{F}_{3}$, to the proper position and record its magnitude and position in Table 9. Determine the uncertainties $\delta m$ and $\delta \theta$ by making an adjustment to the mass and the angle, respectively, until the ring shifts, but doesn't touch the pin, then calculate the uncertainty $\delta F$ by using Eq. (5) and record all these values in Table 9. Write your result in the box below in the form $F_{3} \pm \delta F$ (in N ) at $\theta_{3} \pm \delta \theta$ (in degrees) Compare the experimental and theoretical values for the $F_{3}$ clearly stating the quantitative value you are comparing.
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Solution

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Solution Steps

Step 1: Understanding the Given Data

We have the following data from Table 9:

  • Magnitude of force \( F_3 = 3.4 \, \text{N} \)
  • Angle \( \theta_3 = 72^\circ \)
  • Uncertainty in mass \( \delta m = 0.34 \, \text{kg} \)
  • Uncertainty in angle \( \delta \theta = 3^\circ \)
  • Uncertainty in force \( \delta F = 0.3 \, \text{N} \)
Step 2: Calculating the Uncertainty in Force

The uncertainty in force \( \delta F \) is already provided as \( 0.3 \, \text{N} \). This is calculated using an equation (presumably Eq. (5) from the context), which is not provided here, but we assume it has been correctly applied.

Step 3: Writing the Result in the Required Form

The result should be expressed as \( F_3 \pm \delta F \) at \( \theta_3 \pm \delta \theta \).

Given:

  • \( F_3 = 3.4 \, \text{N} \)
  • \( \delta F = 0.3 \, \text{N} \)
  • \( \theta_3 = 72^\circ \)
  • \( \delta \theta = 3^\circ \)

The result is: \[ F_3 = 3.4 \pm 0.3 \, \text{N} \] \[ \theta_3 = 72 \pm 3^\circ \]

Final Answer

\[ \boxed{F_3 = 3.4 \pm 0.3 \, \text{N} \text{ at } \theta_3 = 72 \pm 3^\circ} \]

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