Question

A 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. It takes 6060 NN 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 3030 degree angle from perpendicular?A 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. It takes 6060 NN 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 3030 degree angle from perpendicular?

Answer 1

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
`F_(\theta ) = 69.28 \ N`

Step-by-step explanation:

From the question we are told that

The length of the wrench is
`L = 30 cm = (30)/(100) = 0.3 \ m`

The distance from the bolt is
`d = 0.30 m`

The force it takes to loosen the bolt is
`F = 60 N`

The angle of application is
`\theta = 30 ^o`

Generally the torque required to loosen the bolt is

`\tau = F * d`

`\tau = 60 * 0.3`

`\tau = 18 Nm`

Now for the bolt to be loosen at
`\theta` the torque at 90° must be the same as that at
`\theta`

So the torque at
`\theta` is mathematically represented as

`\tau = F_(\theta )d cos \theta`

substituting values

`18 = F_(\theta ) * 0.3 cos (30)`

`F_(\theta ) = (18)/(0.3 cos (30))`

`F_(\theta ) = 69.28 \ N`