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Magnitude of Force on Wrench

by dragon18
Tags: force, magnitude, wrench
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dragon18
#1
Feb21-13, 08:20 PM
P: 12
You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 45.0 N*m. Using the data in the figure below (L = 0.300 m and ? = 52.6), determine the magnitude F of the force that you must exert on the wrench.
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Relevant Equations
T = F * d

Attempt
45 = F * cos 52.6 * 0.300m
F = 246.96 N
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Poley
#2
Feb21-13, 08:31 PM
P: 31
What if θ was zero? According to your formula, this would give a torque of Fd (because cos(0) = 1). But, if you look at the picture, if θ = 0, shouldn't the torque be 0 as well? You are just pulling straight out; this shouldn't turn the bolt at all.

Hint: is θ really the angle between the force and the displacement?
dragon18
#3
Feb21-13, 09:09 PM
P: 12
Quote Quote by Poley View Post
What if θ was zero? According to your formula, this would give a torque of Fd (because cos(0) = 1). But, if you look at the picture, if θ = 0, shouldn't the torque be 0 as well? You are just pulling straight out; this shouldn't turn the bolt at all.

Hint: is θ really the angle between the force and the displacement?
If θ=0, then the force would be 150N. θ isn't the angle between the force and displacement, but what am I looking for instead of 52.6?

Poley
#4
Feb21-13, 09:13 PM
P: 31
Magnitude of Force on Wrench

Quote Quote by dragon18 View Post
If θ=0, then the force would be 150N. θ isn't the angle between the force and displacement, but what am I looking for instead of 52.6?
Basically, you want the component of F that is PERPENDICULAR to the displacement. Personally, I wouldn't use cosine but sine. Draw a right triangle with theta, F, and d, and find an expression for the component of F pointing away from d.
dragon18
#5
Feb22-13, 12:57 PM
P: 12
I figured out that the answer is 1.898102N
F=45F*m/(0.300m*sin(52.6))


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