Question

a drill vice uses a threaded bolt to press two plates together with a strong force. it can be used to grip objects while modifying them or to press together two parts while glue dries.
an engineer is designing a drill vice using the bolt in the image. they want the ima of the machine to be 130 when someone applies force at the edge of the handle.
calculate the tpi of the bolt.
tpi =
calculate the pitch of the bolt.
pitch = inches
calculate the maximum radius the handle should have.
r = inches
how would the ima of the system change if the engineer were to apply lubricant to the bolts threads?

Explanation:

Step1: Relate TPI to pitch

Pitch = $\frac{1}{\text{TPI}}$

Step2: Calculate pitch

Pitch = $\frac{1}{5} = 0.2$ inches

Step3: Use IMA formula for screw

IMA = $\frac{2\pi r}{\text{Pitch}}$
Rearrange to solve for $r$: $r = \frac{\text{IMA} \times \text{Pitch}}{2\pi}$

Step4: Substitute values for $r$

$r = \frac{130 \times 0.2}{2\pi} = \frac{26}{6.283} \approx 4.14$ inches

Step5: Analyze IMA and lubrication

IMA depends on geometry, not friction.

Answer:

Calculate the maximum radius the handle should have.
$r \approx 4.14$ inches

How would the IMA of the system change if the engineer were to apply lubricant to the bolt's threads?
The IMA would not change.