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 a: how much force is at the output ram?

Explanation:

Step1: Recall Pascal's Law

Pascal's Law states that pressure is transmitted equally in a fluid, so \( P_A = P_{Output} \), where \( P = \frac{F}{A} \) (pressure = force/area). The area of a piston is \( A = \pi r^2=\frac{\pi d^2}{4} \) (since \( r = \frac{d}{2} \)).

Step2: Calculate Areas

For Piston A: \( d_A = 0.5'' \), so \( A_A=\frac{\pi (0.5)^2}{4} \).
For Output Piston: \( d_O = 2'' \), so \( A_O=\frac{\pi (2)^2}{4} \).

Step3: Set Up Pressure Equality

From \( P_A = P_O \), we have \( \frac{F_A}{A_A}=\frac{F_O}{A_O} \). Solve for \( F_O \):
\( F_O = F_A \times \frac{A_O}{A_A} \). Substitute \( A_A \) and \( A_O \):
\( \frac{A_O}{A_A}=\frac{\frac{\pi (2)^2}{4}}{\frac{\pi (0.5)^2}{4}}=\frac{(2)^2}{(0.5)^2}=\frac{4}{0.25} = 16 \).

Step4: Compute Output Force

\( F_O = 100\ \text{lbs} \times 16 = 1600\ \text{lbs} \).

Answer:

1600 lbs