Complete Question
A 30 cmcm wrench is used to loosen a bolt with a force applied 0.30m from the bolt. It takes 60 N to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30 degree angle from perpendicular?
Answer:
The force required is [tex]F_{\theta } = 69.28 \ N[/tex]
Explanation:
From the question we are told that
The length of the wrench is [tex]L = 30 cm = \frac{30}{100} = 0.3 \ m[/tex]
The distance from the bolt is [tex]d = 0.30 m[/tex]
The force it takes to loosen the bolt is [tex]F = 60 N[/tex]
The angle of application is [tex]\theta = 30 ^o[/tex]
Generally the torque required to loosen the bolt is
[tex]\tau = F * d[/tex]
[tex]\tau = 60 * 0.3[/tex]
[tex]\tau = 18 Nm[/tex]
Now for the bolt to be loosen at [tex]\theta[/tex] the torque at 90° must be the same as that at [tex]\theta[/tex]
So the torque at [tex]\theta[/tex] is mathematically represented as
[tex]\tau = F_{\theta }d cos \theta[/tex]
substituting values
[tex]18 = F_{\theta } * 0.3 cos (30)[/tex]
[tex]F_{\theta } = \frac{18}{0.3 cos (30)}[/tex]
[tex]F_{\theta } = 69.28 \ N[/tex]
