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 asks to calculate the magnitude of the torque applied when a car mechanic applies a force of 800 N to a wrench, with the distance from the bolt to her hand being 0.40 m. The force is applied perpendicular to the arm of the wrench. We need to use the formula for torque, which is the product of the force and the distance (lever arm).
Answer
The torque applied is $320 \text{ N⋅m}$.
Answer for screen readers
The magnitude of the torque applied is $320 \text{ N⋅m}$.
Steps to Solve
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Write down the formula for torque
Torque ($\tau$) is calculated as the product of the force ($F$) and the distance from the pivot point (lever arm, $r$). Since the force is applied perpendicularly, we can use the formula: $$ \tau = r \times F $$
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Identify the given values
Force, $F = 800$ N Distance (lever arm), $r = 0.40$ m
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Substitute the values into the formula
$$ \tau = 0.40 \text{ m} \times 800 \text{ N} $$
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Calculate the torque
$$ \tau = 320 \text{ N⋅m} $$
The magnitude of the torque applied is $320 \text{ N⋅m}$.
More Information
Torque is a rotational force or the measure of the force that can cause an object to rotate about an axis. It is measured in Newton-meters (N⋅m).
Tips
A common mistake is forgetting the units. Torque is measured in Newton-meters, not just Newtons or meters. Also, it is crucial to ensure that the force and distance are in standard units (Newtons and meters, respectively) before performing the calculation.
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