Question

How much force needs to be applied to a small piston with a radius of 2 in so that a large piston of 8 in can raise 300lbs? What is the pressure exerted on the small piston?

Answer 1

To calculate the force needed to raise the large piston using the small piston, we can use Pascal's law and the formula for force. The force needed is 4800 lbs and the pressure exerted on the small piston is approximately 382.72 psi.

Step-by-step explanation:

To calculate the force needed to raise the large piston using the small piston, we can use Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions. The formula for force in this case is:

Forcesmall = (Forcelarge * Arealarge) / Areasmall

Given that the radius of the small piston is 2 in and the radius of the large piston is 8 in, the areas can be calculated as follows:

Areasmall = π * (2 in)2 = 4π in2

Arealarge = π * (8 in)2 = 64π in2

Substituting the values into the formula:

Forcesmall = (300 lbs * 64π in2) / 4π in2 = 4800 lbs

The pressure exerted on the small piston can be calculated using the formula:

Pressure = Force / Area

Pressure = 4800 lbs / 4π in2 ≈ 382.72 psi