3. The following data refer to a single-acting hydraulic press: Force exerted on ram piston = 5200 N. Force exerted to plunger = 365 N. Diameter of the plunger = 8 cm. Stroke length of plunger piston = 10cm. Use the given information to answer the following questions: a) Calculate the diameter of the ram piston.
To calculate the diameter of the ram piston, we can use the formula for the area of a circle.
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
First, let's calculate the area of the plunger using the given diameter of 8 cm.
The diameter of the plunger is 8 cm, so the radius is half of that, or 4 cm.
So, the area of the plunger is A = π(4 cm)² = 16π cm².
Now, let's calculate the area of the ram piston using the formula for force: force = pressure × area.
The force exerted on the ram piston is given as 5200 N, and the force exerted to the plunger is 365 N.
The area of the plunger is 16π cm².
To find the diameter of the ram piston, we need to find its radius. Let's assume the radius of the ram piston is r cm.
Using the formula for force, we can set up an equation: (365 N)/(16π cm²) = (5200 N)/(πr² cm²).
Simplifying the equation, we get: 365/(16π) = 5200/r².
Cross-multiplying, we get: r² = (5200 * 16π)/365.
Calculating this value, we get: r² ≈ 398.15.
Taking the square root of both sides, we get: r ≈ √398.15 = 19.95 cm.
Finally, we can calculate the diameter of the ram piston by multiplying the radius by 2.
The diameter of the ram piston is 2 * 19.95 cm = 39.9 cm.