a hydraulic jack is used to move an 8896 newton car. if the area of the output piston is 8 times that of the input piston, how much input force is required to lift the car. i did Pi * 8 them multiplied that answer * 8896 then divided that answer times 8896. i don't think that is right please help
To solve this problem, you need to apply the principle of Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.
In the case of a hydraulic jack, the input force is applied to a smaller piston, and through the transmission of pressure, it generates a larger output force on the larger piston.
Let's assume the area of the input piston is A1, and the area of the output piston is A2. Given that the area of the output piston is 8 times that of the input piston (A2 = 8A1), we can write the equation:
Force1 / A1 = Force2 / A2
Where Force1 is the input force and Force2 is the output force.
In this case, we know the output force (Force2) is 8896 N, and we need to determine the input force (Force1).
Substituting the given values into the equation:
Force1 / A1 = 8896 N / (8A1)
Next, we can rearrange the equation to solve for the input force:
Force1 = (8896 N / (8A1)) * A1
Simplifying the equation:
Force1 = 8896 N / 8
So, the input force required to lift the car is 1112 N.
Therefore, your calculation should be as follows:
Input force = Output Force / 8
Input force = 8896 N / 8 = 1112 N
Hence, an input force of 1112 Newtons is required to lift the car using the hydraulic jack.