"To lift an object weighing 12,000N, how much force is needed on a piston with an area of 0.060 m^2 if the platform being lifted has an area of 3.0 m^2?"
240
To lift an object weighing 12,000 N, you need to determine the force that is required on a piston with a given area. This can be done using Pascal's law, which states that pressure is equal to force divided by the area.
First, we need to calculate the pressure exerted by the object on the platform. The pressure is given by the formula:
Pressure = Force / Area
Given that the force is 12,000 N and the area of the platform is 3.0 m^2, we can substitute these values into the formula:
Pressure = 12,000 N / 3.0 m^2
Pressure = 4000 N/m^2 (Pascal)
Now, since the pressure in a hydraulic system is transmitted equally in all directions, the pressure exerted on the piston will be the same as the pressure on the platform. Therefore, the pressure on the piston will also be 4000 N/m^2.
Finally, we can determine the force needed on the piston using the formula:
Force = Pressure × Area
Given that the area of the piston is 0.060 m^2, we can substitute the values into the formula:
Force = 4000 N/m^2 × 0.060 m^2
Force = 240 N
Therefore, a force of 240 Newtons is needed on the piston to lift an object weighing 12,000 Newtons.