A wrench with a length of #42 cm# is being used to unscrew a #7/2 cm# bolt. If a torque of #42 N*m# 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
Aug 7, 2017

Answer:

#F=100N#

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(blue)(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 #F#.

#color(red)(F=tau/(rsinphi))#

We are provided the following information:

#"r"=42"cm"=0.42"m"#

#tau=42"Nm"#

And it is implied that #phi=90^o# since no angle—nor the necessary information to calculate one—is provided.

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 screw and not the head of the screw.

Therefore, we have:

#F=(42"Nm")/(0.42"m")#

#=100"N"#