Calculate Min Angle to Exert 35.0 NM Torque with 355 N Force

[lacar213]

Homework Statement

You want to exert a torque of at least 35.0 N·m on a wrench whose handle is 0.150 m long. If you can provide a force of 355 N to the end of the wrench, what is the minimum angle at which you can apply the force in order to achieve the desired torque?

Homework Equations

t = rfsinθ

The Attempt at a Solution

I am not sure how to rearrange this equation to find the angle or what other equation I have to use to find the angle.
torque = 35.0 NM
F = 355 N
M = .150 M

 

[asleight]

Homework Statement

You want to exert a torque of at least 35.0 N·m on a wrench whose handle is 0.150 m long. If you can provide a force of 355 N to the end of the wrench, what is the minimum angle at which you can apply the force in order to achieve the desired torque?

Homework Equations

t = rfsinθ

The Attempt at a Solution

I am not sure how to rearrange this equation to find the angle or what other equation I have to use to find the angle.
torque = 35.0 NM
F = 355 N
M = .150 M

$$\vec{\tau}=\vec{r}\times\vec{F}\rightarrow\frac{\vec{\tau}}{rF}=\sin(\theta)$$...

 

[lacar213]

After you divide the torque by the length and force do you take the sin of that answer - because when you do it is very small??

 

[asleight]

After you divide the torque by the length and force do you take the sin of that answer - because when you do it is very small??

You apply the arcsin function to both sides of the equation, yielding:

$$\arcsin\left(\frac{\vec{\tau}}{rF}\right)=\theta$$.