2. A hydraulic press has a plunger diameter of 3 and a ram diameter of 10 cm. The handle lengths are y = 40 cm and x = 10 cm. The plunger stroke is 8 cm and the force applied at the handle is 270 Ν. In pairs with your partner: a) Calculate the ram force output.
To calculate the ram force output, we can use the principle of Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted equally in all directions.
First, let's calculate the ratio of the plunger area (A1) to the ram area (A2) using the formula:
A1/A2 = (d1^2) / (d2^2)
where d1 is the diameter of the plunger and d2 is the diameter of the ram.
Plunger diameter (d1) = 3 cm
Ram diameter (d2) = 10 cm
A1/A2 = (3^2) / (10^2)
A1/A2 = 9 / 100
A1/A2 = 0.09
Next, let's find the plunger force (F1) using the formula:
F1 = A1 * P1
where P1 is the pressure applied to the plunger. Since the pressure is transmitted equally in all directions, P1 is the force applied at the handle divided by the handle area.
Handle length (y) = 40 cm
Plunger stroke (s) = 8 cm
Plunger area (A1) = π * (d1^2) / 4
A1 = π * (3^2) / 4
A1 = 7.07 cm^2
Handle area (Ah) = y * x
Ah = 40 cm * 10 cm
Ah = 400 cm^2
P1 = 270 N / 400 cm^2
P1 = 0.675 N/cm^2
F1 = A1 * P1
F1 = 7.07 cm^2 * 0.675 N/cm^2
F1 = 4.78 N
Now, we can find the ram force (F2) using the formula:
F2 = A2 * P2
where P2 is the pressure applied to the ram. Since the pressure is transmitted equally, P2 is the same as P1.
F2 = A2 * P1
F2 = (A1 / A2) * F1
F2 = 0.09 * 4.78 N
F2 = 0.43 N
Therefore, the ram force output is 0.43 N.