To calculate the torque exerted by the force on the root of the tooth about point $A$, we’ll use the torque formula:

$\tau = r \cdot F \cdot \sin(\theta)$

where:

• $r = 1.20 \, \text{cm} = 0.012 \, \text{m}$ (distance from point $A$ to point $B$),
• $F = 73.2 \, \text{N}$ (magnitude of the force),
• $\theta = 48.0^\circ$ (angle between the force and the line connecting points $A$ and $B$).

Step-by-Step Calculation

1. Convert the distance to meters (if not already in meters): $r = 1.20 \, \text{cm} = 0.012 \, \text{m}$

2. Calculate the sine of the angle: $\sin(48.0^\circ) \approx 0.7431$

3. Calculate the torque: $\tau = 0.012 \, \text{m} \cdot 73.2 \, \text{N} \cdot 0.7431$

   Performing this calculation:

   $\tau \approx 0.012 \times 73.2 \times 0.7431 \approx 0.6537 \, \text{N}\cdot\text{m}$

Answer

The torque exerted on the root of the tooth about point $A$ is approximately: $\tau \approx 0.654 \, \text{N}\cdot\text{m}$

Would you like further explanation on torque concepts or other related topics?

Here are five related questions for further understanding:

1. How does changing the angle of the force affect the torque generated?
2. What would happen to the torque if the force were applied at a different point on the tooth?
3. Why is the sine of the angle used in calculating torque?
4. How does torque relate to rotational equilibrium in systems?
5. What are some practical applications of torque in dental mechanics?

Tip: Always convert distances to meters in physics calculations to ensure consistency in SI units.