**Problem Statement:**A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 13 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench.**Diagram Explanation:**The diagram illustrates a wrench with a lever arm of 0.30 meters. The force \( \vec{F} \) is applied at a 60° angle to the lever arm. The task is to find the magnitude of force \( \vec{F} \) that results in a torque of 13 N · m.**Key Details:**- Torque required: 13 N · m- Length of lever arm: 0.30 m- Angle of applied force: 60°\[ \text{Force ( } \vec{F} \text{) = } \underline{\hspace{3cm}} \text{ N} \]Use the formula for torque: \[ \tau = r \times F \times \sin(\theta) \]Where:- \( \tau \) = torque - \( r \) = distance from pivot point (lever arm length)- \( F \) = force- \( \theta \) = angle between force and lever arm (60° in this case)

Given data: The magnitude of the torque required is T=13 N-m. The distance of force applied from spark plug is d=0.30 m. The angle made by force with wrench is θ=60o. The expression for the force exerted on the wrench can be calculated as, T=F×sinθ×dSubstitute the known values in the above expression. 13 N·m=F×sin60o×0.30 mF=13 N·m0.2598 mF=50.03 N Thus, the force exerted on the wrench is 50.03 N.

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A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 13 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench. 0.30 m 60 N

A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 13 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench. 0.30 m 60 N

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Problem Statement:**

A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 13 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench.

**Diagram Explanation:**

The diagram illustrates a wrench with a lever arm of 0.30 meters. The force \( \vec{F} \) is applied at a 60° angle to the lever arm. The task is to find the magnitude of force \( \vec{F} \) that results in a torque of 13 N · m.

**Key Details:**

- Torque required: 13 N · m
- Length of lever arm: 0.30 m
- Angle of applied force: 60°

\[ \text{Force ( } \vec{F} \text{) = } \underline{\hspace{3cm}} \text{ N} \]

Use the formula for torque:
\[ \tau = r \times F \times \sin(\theta) \]

Where:
- \( \tau \) = torque
- \( r \) = distance from pivot point (lever arm length)
- \( F \) = force
- \( \theta \) = angle between force and lever arm (60° in this case)

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