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: b) Calculate the number of plunger strokes required to lift the ram 12 cm.

Answer 1

To calculate the number of plunger strokes required to lift the ram 12 cm, we need to determine the ratio of the plunger stroke to the ram stroke.

Given:
Plunger diameter (Dp) = 3 cm
Ram diameter (Dr) = 10 cm
Plunger stroke (Sp) = 8 cm
Ram lift (Sl) = 12 cm

First, let's find the area of the plunger and the area of the ram.

Area of plunger (Ap) = π * (Dp/2)^2
= π * (3/2)^2
= 7.07 cm^2

Area of ram (Ar) = π * (Dr/2)^2
= π * (10/2)^2
= 78.54 cm^2

Next, we can calculate the ratio of the plunger stroke to the ram lift.

Stroke ratio = Sp/Sl
= 8/12
= 2/3

Therefore, for every 2 plunger strokes, the ram will lift by 3 cm.

To lift the ram by 12 cm, we can set up a proportion:

2 plunger strokes / 3 cm = X plunger strokes / 12 cm

Cross-multiplying:
2 * 12 cm = 3 * X plunger strokes

24 cm = 3 X plunger strokes

Dividing by 3:
X plunger strokes = 24 cm / 3 cm
= 8

Therefore, it will take 8 plunger strokes to lift the ram by 12 cm.