Question

s screw jack is a device which uses a screw system to lift very heavy objects such as automobiles.
an engineer is using a screw jack to lift a load by turning the handle counter clockwise exactly one rotation. they apply
their effort force at the edge of the handle.
calculate the distance the effort force travels (exactly one rotation).
d_e = inches
calculate the tpi of the screw.
tpi =
calculate the pitch of the screw.
pitch = inches
find the ima of the screw jack.
ima =
how would the ima of the screw jack change if it was lifting a load with twice as much weight?
the ima would not change

Explanation:

Step1: Calculate effort distance

The effort moves in a circle with radius 16 in. The circumference is $C=2\pi r$.
$d_E = 2\pi \times 16 = 32\pi \approx 100.53$ inches

Step2: Calculate TPI of the screw

TPI (threads per inch) is total threads over length.
From the diagram, total threads = 7, length = 1.4 in.
$\text{TPI} = \frac{7}{1.4} = 5$

Step3: Calculate screw pitch

Pitch is inverse of TPI.
$\text{Pitch} = \frac{1}{\text{TPI}} = \frac{1}{5} = 0.2$ inches

Step4: Calculate IMA of screw jack

IMA is effort distance over pitch.
$\text{IMA} = \frac{d_E}{\text{Pitch}} = \frac{32\pi}{0.2} = 160\pi \approx 502.65$

Step5: Analyze IMA vs load weight

IMA is a mechanical advantage based on the screw and handle dimensions, not load weight.

Answer:

$d_E = 100.53$ inches
$\text{TPI} = 5$
$\text{Pitch} = 0.2$ inches
$\text{IMA} = 502.65$
The IMA would not change