A hydraulic press has a ram of 30 cm diameter and the plunger of 4.5 cm diameter Find the weight lifted by the hydraulic press when the forces applied at the plunger is 500 N.
To find the weight lifted by the hydraulic press, we need to use the principles of Pascal's law and the formula for pressure.
Pascal's law states that when pressure is applied to a fluid in a confined space, the pressure is transmitted equally in all directions. In the case of a hydraulic press, this means that the pressure applied to the small plunger will be transmitted to the larger ram.
We can use the formula for pressure:
Pressure = Force / Area
Let's first calculate the area of the plunger and the area of the ram:
Area of the plunger = π * (radius of the plunger)^2
= π * (4.5 cm / 2)^2
= 7.95 cm^2
Area of the ram = π * (radius of the ram)^2
= π * (30 cm / 2)^2
= 706.86 cm^2
Now, let's calculate the pressure applied to the fluid by the plunger:
Pressure = Force / Area of the plunger
= 500 N / 7.95 cm^2
Convert the pressure to pascals by dividing by 10000 (1 N/cm^2 = 10000 Pascals):
Pressure = 500 N / 7.95 cm^2 / 10000 cm^2 / m^2
= 6.29 Pa
Since the pressure is transmitted equally in all directions, the pressure at the ram will also be 6.29 Pa.
Now, let's calculate the force exerted by the ram:
Force = Pressure * Area of the ram
= 6.29 Pa * 706.86 cm^2
Convert the force to newtons by multiplying by 10000:
Force = 6.29 Pa * 706.86 cm^2 * 10000 cm^2 / m^2
= 4,442,406 N
Therefore, the weight lifted by the hydraulic press when the force applied at the plunger is 500 N is approximately 4,442,406 N.