calculate the force output by the larger piston of a hydraulic lift when a force of 700 newtons is excerted on the smaller piston and the areas of the two pistons are 20cm and 950cm squared.
To calculate the force output by the larger piston of a hydraulic lift, we can use Pascal's law, which states that the pressure in a fluid at rest is transmitted equally in all directions.
First, let's determine the pressure exerted on the smaller piston using the formula:
Pressure = Force / Area
The force exerted on the smaller piston is given as 700 newtons, and the area of the smaller piston is 20 cm^2. We need to convert the area to square meters before calculating the pressure.
Area = 20 cm^2 = 20 / 10000 m^2 = 0.002 m^2
Now we can calculate the pressure:
Pressure = 700 N / 0.002 m^2 = 350,000 N/m^2 (Pa)
Since the pressure is transmitted equally to all parts of the fluid, the same pressure will act on the larger piston. To find the force output by the larger piston, we can use the formula:
Force = Pressure × Area
The area of the larger piston is given as 950 cm^2. Again, we need to convert the area to square meters before calculating the force.
Area = 950 cm^2 = 950 / 10000 m^2 = 0.095 m^2
Now we can calculate the force:
Force = 350,000 N/m^2 × 0.095 m^2 = 33,250 N
Therefore, the force output by the larger piston of the hydraulic lift is 33,250 newtons.