A wrench with a length of #42 cm# is being used to unscrew a #7/2 cm# bolt. If a torque of #32 Nm# is needed to overcome the friction keeping the bolt in place, what is the minimum torque that must be applied to the wrench to unscrew the bolt?
1 Answer
Answer:
Explanation:
I assume the question is meant to ask what is the minimum force required to unscrew the bolt.
Torque is given by the equation:
#color(darkblue)(tau=rFsinphi)# where
#F# is the applied force,#r# is the distance from the pivot (axis of rotation) that the force is applied, and#phi# is the angle at which the force is applied.
We can rearrange the equation for torque to find
#color(crimson)(F=tau/(rsinphi))#
We are provided the following information:

#>"r"=42"cm"=0.42"m"# 
#>tau=32"Nm"#
And it is implied that
Note that I am not including the radius of the bolt in the measurement of the total radius because I am assuming that this is the radius of the body of the bolt and not the head of the bolt.
Therefore, we have:
#F=(32"Nm")/(0.42"m")#
#=76.19"N"#
#~~76"N"#