a container weighing a 1.20 x 10^4 N sits on a hydraulic press piston with can area of 0.80m^2. Compressed ir exerts a force of on the second piston which has an area of 0.30m^2 How large must this force be to support the car
To determine the force required to support the car on the second piston, we can use the principle of Pascal's law, which states that the pressure applied to a fluid in a confined space is transmitted equally everywhere in the fluid.
First, let's simplify the given values to their standard form:
Weight of the container = 1.20 x 10^4 N
Area of the first piston (A1) = 0.80 m^2
Area of the second piston (A2) = 0.30 m^2
Using Pascal's law, we can equate the pressures on the two pistons:
Pressure1 = Pressure2
Pressure1 is given by the weight divided by the area of the first piston:
Pressure1 = Weight of the container / Area of piston 1
Pressure1 = 1.20 x 10^4 N / 0.80 m^2
Pressure2 is the force exerted on the second piston divided by the area of the second piston:
Pressure2 = Force on piston 2 / Area of piston 2
Since the pressure is equal in both cases, we can set up the equation:
Weight of the container / Area of piston 1 = Force on piston 2 / Area of piston 2
Now we can solve for the force on the second piston:
Force on piston 2 = (Weight of the container / Area of piston 1) * Area of piston 2
Force on piston 2 = (1.20 x 10^4 N / 0.80 m^2) * 0.30 m^2
Calculating this expression will give us the force required to support the car on the second piston.