work distance effort

Question

5.2 The diameter of the ram piston of a press is 125 mm and that of the plunger is 25 mm. The mechanical advantage on the plunger is 16. The stroke length of the plunger is 50 mm. Calculate the following: 5.2.1 The effort that has to be applied to the handle in order to lift a load of 500 kg 5.2.2 The distance the load will be raised after 50 strokes of the plunger 5.2.3 The work done by the press to lift the load of 500 kg after 50 strokes. The efficiency of the press is only 80%.

Answer 1

(5.2.1)

Mass of the Load = 500 kg.

Mechanical Advantage of the Plunger = 16

We know that Mechanical advantage = Weight lift by the Plunger / Force applied on the plunger.

Force applied on the plunger = Weight lift by the Plunger / Mechanical advantage.

F = 500 / 16

F = 31.25 kN.

Force applied in order to lift the load F = 31.25 kN.

Answer 2

(5.2.2)

The diameter of the Ram = 125 mm.

Diameter of the Plunger = 25 mm

Number of strokes = 60 mm

Stroke length of the Plunger = 50 mm =0.05 m

Radius of the Ram = 125 / 2 = 62.5 mm = 0.0625 m

Radius of the Plunger = 25 / 2 = 12.5mm = 0.0125 mm

Area of the Ram = πr² = π(0.0625)²

Area of the Ram = 0.01227 m²

Area of the Plunger = πr² = π(0.0125)² = 4.9 * 10^-4.

Let the distance travelled by the weight per stroke = x mts.

Volume displaced by ram = Area of the ram * Distance

Volume displaced by ram = 0.01227 x m³.

Volume displaced by Plunger = Area of the Plunger * stroke length

Volume displaced by Plunger = 4.9 * 10^-4 * 0.05

Volume displaced by Plunger = 2.454 * 10^-5 m³

As we know that volume of the plunger and ram are equal when there is no slip.

2.454 * 10^-5 m³ = 0.01227 x

x = 500 per stroke.

Distance travelled for 60 mm = 500 * 0.06

Distance travelled = 30 m.

Distance travelled to lift the wieght = 30m.

Answer 3

(5.2.3)

The diameter of the Ram = 125 mm.

Diameter of the Plunger = 25 mm

Number of strokes = 60 mm

Stroke length of the Plunger = 50 mm =0.05 m

Efficiency = 80%

Radius of the Ram = 125 / 2 = 62.5 mm = 0.0625 m

Radius of the Plunger = 25 / 2 = 12.5mm = 0.0125 mm

Area of the Ram = πr² = π(0.0625)²

Area of the Ram = 0.01227 m²

Area of the Plunger = πr² = π(0.0125)² = 4.9 * 10^-4.

Let the distance travelled by the weight per stroke = x mts.

Volume displaced by ram = Area of the ram * Distance

Volume displaced by ram = 0.01227 x m³.

Volume displaced by Plunger = Area of the Plunger * stroke length

Volume displaced by Plunger = 4.9 * 10^-4 * 0.05

Volume displaced by Plunger = 2.454 * 10^-5 m³

As we know that volume of the plunger and ram are equal when there is no slip.

2.454 * 10^-5 m³ = 0.01227 x

x = 500 per stroke.

Distance travelled for 60 mm = 500 * 0.06

Distance travelled = 30 m.

Distance travelled to lift the wieght = 30m.

Work done = weight lift * Distance travelled

Work done = 500 * 30 = 1500 Nm.

Efficiency = (Output work/ input work) * 100

Input work = Output work / (Efficiency / 100)

Pin = 1500 / (80/100)

Work done  = 1875 Nm.

Work done by the press to lift the load = 1875 Nm.