Question

The radii of the press plunger and pump plunger are in a ratio of 50:14. If an effort of 20 kgf acts on the pump plunger, calculate the maximum effort that the press plunger can overcome.

Answer 1

Step 1. Given data

Ratio of the radius of the press plunger and the radius of the pump plunger $=\frac{R}{r}=\frac{50}{14}$

Effort on the plunger, $E=20kgf$

Maximum effort that the plunger can overcome, $L=?$

Step 2. Formula used

$\frac{L}{E}={\left(\frac{R}{r}\right)}^2$ …………………….(a)

Step 3. Calculation of the maximum effort that the press plunger can overcome

Substituting the given values in equation (a), we get

$$\begin{gathered} \frac{L}{20kgf}={\left(\frac{50}{14}\right)}^2 \\ L=20\times 12.755kgf \\ L=255kgf \end{gathered}$$

Step 4. Final answer

Hence, the maximum effort that the press plunger can overcome is equal to 255 kgf.