Calculating Force for Torque: Understanding Proper Spark Plug Tightening

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To calculate the force required for proper spark plug tightening, the torque specified is 26 N·m, and the lever arm length is 0.28 m. The initial calculation incorrectly used the lever arm length instead of the perpendicular distance. The correct perpendicular distance must be determined using trigonometry from the right triangle formed by the wrench, with a hypotenuse of 0.28 m and an angle of 50 degrees. This leads to the conclusion that the perpendicular distance is approximately 0.16165 m, which is crucial for accurately calculating the force. Understanding the correct application of torque and the geometry involved is essential for achieving the proper tightening of spark plugs.
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1. 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 26 N·m. Using the data in the drawing, determine the magnitude F of the force that you must exert on the wrench.



2. Torque= Force * Lever arm length



3. The force is said to be 26 N*m, and the lever arm length is shown to be 0.28 cm in the picture.

26 N*m = F * 0.28 m
F= 26 N*m/0.28m
F= 92.86 N

Which is wrong. What did I do wrong?
 

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0.28 is the length of it, not the perpendicular distance. What is the perpendicular distance it nust move?
 
Is it 16.165 cm (.16165 m)?
 
IAmSparticus said:
Is it 16.165 cm (.16165 m)?

How did you get that?

The wrench forms a right angled triangle with hypotenuse 0.28 which makes an angle of 50 with the horizontal.
 

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