A hydraulic jack is used to lift a 2600 pound car. If the output piston (the one the car is sitting on) has an area of 60 square inches, how much force must be applied to the 0.5 square inch input piston to lift the car? ______ pounds.
To determine the force that needs to be applied to the 0.5 square inch input piston, we can use the principle of Pascal's law. According to Pascal's law, the pressure exerted on a fluid in a confined space is transmitted equally in all directions.
In this case, the fluid in the hydraulic jack is transmitting the pressure from the input piston to the output piston, which is lifting the car. We can use the equation:
Pressure = Force / Area
Since the pressure is transmitted equally, the pressure on the input piston is the same as the pressure on the output piston. If we let P represent the pressure, then we can set up the equation:
P(input) = P(output)
Now we can substitute the values we have:
Force(input) / Area(input) = Force(output) / Area(output)
Plugging in the given values:
Force(input) / 0.5 square inch = 2600 pounds / 60 square inches
To solve for Force(input), we can cross-multiply and then divide:
Force(input) = (0.5 square inch * 2600 pounds) / 60 square inches
Calculating the result:
Force(input) = 21.67 pounds
Therefore, the force that must be applied to the 0.5 square inch input piston to lift the car is approximately 21.67 pounds.