To find the magnitude of the torque exerted on the door, follow these steps:
1. Understand the scenario: A person exerts a force of 40 N at the end of a door that is 92 cm wide. Since the force is applied perpendicularly, the full length of the door acts as the lever arm.
2. Convert the units: The width of the door is given in centimeters, but we need it in meters to use standard units for calculating torque.
[tex]\[
\text{Distance} = 92 \, \text{cm} = 92 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.92 \, \text{m}
\][/tex]
3. Apply the torque formula: Torque ([tex]\(\tau\)[/tex]) is given by the formula:
[tex]\[
\tau = \text{Force} \times \text{Distance}
\][/tex]
where the force is 40 N and the distance is 0.92 m.
4. Calculate the torque:
[tex]\[
\tau = 40 \, \text{N} \times 0.92 \, \text{m} = 36.800000000000004 \, \text{Nm}
\][/tex]
5. Express the answer with two significant figures: Rounding 36.800000000000004 Nm to two significant figures, we get:
[tex]\[
\tau \approx 37 \, \text{Nm}
\][/tex]
Therefore, the magnitude of the torque exerted on the door is [tex]\(37 \, \text{Nm}\)[/tex] when rounded to two significant figures.
