(a) If a 22 pound baby sits atop a 1 ft^2 piston that is connected to a 10 ft^2 platform via sealed, water filled pipes, how heavy and massive of a car can the baby's weight lift (answer in pounds, Newtons, and Kilograms)?
(b) If the baby's initial height on the piston is 10 ft, how high will the car be raised after the baby's piston is completely compressed?
P1 = P2
Let baby sitting on 1ft^2 platform be P1 --> 22lbs/144in^2 = .153 lbs/in^2
Let car on platform be P2 -->
weight of car/14400in^2 =P2
--> weight of car = 14400in^2 X .153 lbs/in^2 = 2,203.2 lbs.
I assumed pounds in this problem meant pounds force rather than pounds mass. 1 pound force = 4.45 N so 22 lb = 97.9 N, and the mass that would give 97.9 N is 97.9N/9.8m/s^2 = 9.99 kg
If the baby\'s piston is completely compressed, the volume of water the baby\'s piston held will now be in the other piston - the one holding the car on a platform. First you figure out what volume of water would be in the baby's piston before it was compressed. So you had a cylinder with a cross sectional area of 1 ft^2 and a height of 10 ft, so that is a volume of 1ft^2X10ft = 10ft^3.
That\'s the volume that will be transferred to the other cylinder, but since that cylinder has a larger cross sectional area, the height the water will rise will be less than 10 ft.
Volume = Area of base times height
10ft^3 = 10ft^2 X H -->
H = 1 ft. The car will be raised 1 ft.
Are my answers/solutions correct?? Or did I make a mistake? Please help me...thanks in advance!