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Turning a bolt with a wrench produces a torque vector that drives the bolt forward. The magnitude of the torque vector is rFsinθ, where r is the vector along the handle of the wrench, F is the force vector applied to the handle of the wrench, and θ is the angle between these two vectors. Therefore, the magnitude of the torque is r×F. In Exercises 60 and 61, find the magnitude of the torque. Express each answer in foot-pounds.

A force of 20 lb is applied to a wrench with a 6-inch handle at an angle of 60.

Short Answer

Expert verified

The magnitude of the torque is 53foot-pounds.

Step by step solution

01

Step 1. Given Information

Turning a bolt with a wrench produces a torque vector that drives the bolt forward. The magnitude of the torque vector is rFsinθ, where r is the vector along the handle of the wrench, F is the force vector applied to the handle of the wrench, and θ is the angle between these two vectors. Therefore, the magnitude of the torque is r×F. We have to find the magnitude of the torque. and expressing answer in foot-pounds.

A force of 20 lb is applied to a wrench with a 6-inch handle at an angle of 60.

02

Step 2. Now finding the magnitude of the torque. 

rFsinθ

From the question r=6-inch,F=20lb,θ=60o

role="math" localid="1649784087723" rFsinθ=620sin60orFsinθ=6×20×sin60orFsinθ=6×20×32rFsinθ=6×10×3rFsinθ=603in-lb

03

Step 3. We have to convert the answer in foot-pounds. 

As we know to convert in foot-pounds take your foot-lb figure and divide by 12.

rFsinθ=60123foot-poundsrFsinθ=53foot-pounds

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