A 30 cm wrench is used to loosen a bolt with a force applied 0.30 mm 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?

Respuesta :

Answer:

The applied force is 69.28 N.

Explanation:

Given that,

Distance = 30 cm

Force = 60 N

Distance = 0.30 m

We need to calculate the torque to loosen the bolt

Using formula of torque

[tex]\tau=F\times d[/tex]

Where, F = force

d = distance

Put the value into the formula

[tex]\tau=60\times0.30[/tex]

[tex]\tau=18\ N-m[/tex]

We need to calculate the force

To get the same torque with a force applied at 30 degree

Using formula of torque again

[tex]18=F\times0.30\times\cos30^{\circ}[/tex]

[tex]F=\dfrac{18}{0.30\times\cos30^{\circ}}[/tex]

[tex]F=69.28\ N[/tex]

Hence, The applied force is 69.28 N.