Question

piston a has .5\ diameter
piston b has 1\ diameter
output piston has 2\ diameter

what if 100 lbs of force is applied to ram input b: how much force is at the output ram?

Explanation:

Step1: Recall Pascal's Law (Pressure is equal)

Pressure \( P = \frac{F}{A} \), so \( \frac{F_B}{A_B} = \frac{F_{output}}{A_{output}} \), where \( A = \pi (\frac{d}{2})^2 \).

Step2: Calculate areas of Piston B and Output Piston

For Piston B: \( d_B = 1'' \), \( A_B = \pi (\frac{1}{2})^2 = \frac{\pi}{4} \) in².
For Output Piston: \( d_{output} = 2'' \), \( A_{output} = \pi (\frac{2}{2})^2 = \pi \) in².

Step3: Solve for \( F_{output} \)

From \( \frac{F_B}{A_B} = \frac{F_{output}}{A_{output}} \), rearrange: \( F_{output} = F_B \times \frac{A_{output}}{A_B} \).
Substitute values: \( F_{output} = 100 \times \frac{\pi}{\frac{\pi}{4}} = 100 \times 4 = 400 \) lbs.

Answer:

400 lbs