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.
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.