A car mechanic applies a force of 800 N to a wrench to loosen a bolt. She applies the force perpendicular to the arm of the wrench. The distance from the bolt to her hand is 0.40 m... A car mechanic applies a force of 800 N to a wrench to loosen a bolt. She applies the force perpendicular to the arm of the wrench. The distance from the bolt to her hand is 0.40 m. What is the magnitude of the torque applied?
Understand the Problem
The question describes a scenario where a car mechanic applies a force to a wrench. It provides the magnitude of the force and the distance from the bolt to her hand, which is the length of the wrench arm. It asks us to calculate the magnitude of the torque applied to the wrench, given the applied force and the length of the wrench arm. The formula for torque is torque = force x distance.
Answer
The magnitude of the torque applied is $320 \, \text{N} \cdot \text{m}$.
Answer for screen readers
The magnitude of the torque applied is $320 , \text{N} \cdot \text{m}$.
Steps to Solve
- Identify the given values
The problem states that the force applied is $800 , \text{N}$ and the distance from the bolt to the hand is $0.40 , \text{m}$.
- Apply the torque formula
The formula for torque ($\tau$) is given by:
$ \tau = F \cdot d $
where $F$ is the force applied and $d$ is the distance from the axis of rotation (the bolt) to the point where the force is applied.
- Substitute the given values into the formula
Substitute $F = 800 , \text{N}$ and $d = 0.40 , \text{m}$ into the torque formula:
$ \tau = 800 , \text{N} \cdot 0.40 , \text{m} $
- Calculate the torque
$ \tau = 320 , \text{N} \cdot \text{m} $
The magnitude of the torque applied is $320 , \text{N} \cdot \text{m}$.
More Information
Torque is a twisting force that causes rotation. The unit for torque is Newton-meter (N⋅m).
Tips
A common mistake is using the wrong formula or mixing up the force and distance values in the torque equation. Ensure you use the correct formula ($\tau = F \cdot d$) and plug in the correct values for force and distance. Also, forgetting to include units can be a problem.
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