a hydraulic press contains oil of density=800kg/meter cube,and the areas of the large cylinder=0.5meter squad and area of small cylinder=0.0001meter squad.the mass of the large piston is 51kg,while the small piston has unknown mass m.If an additonal mass of 510kg is placed on the large piston,the press is in balance with the small piston a height of 1m above the large one.find mass m

0.032

To find the mass of the small piston (m), we can use the principle of Pascal's Law, which states that the pressure applied to a fluid enclosed in a container is transmitted undiminished to all portions of the fluid and to the walls of its container.

Here's how to solve the problem step by step:

Step 1: Calculate the pressure applied by the additional mass on the large piston.

The pressure exerted by the additional mass can be calculated using the formula:
Pressure = Force / Area

Since the force exerted is the weight of the additional mass (510 kg) and the area of the large piston is 0.5 m^2, we can use the formula to calculate the pressure:
Pressure on large piston = (510 kg) * (9.8 m/s^2) / (0.5 m^2)

Step 2: Apply Pascal's Law to find the pressure on the small piston.

According to Pascal's Law, the pressure is transmitted undiminished throughout the fluid. Therefore, the pressure on the small piston will be the same as the pressure on the large piston.

Pressure on small piston = Pressure on large piston

Step 3: Calculate the force exerted on the small piston.

The force exerted on the small piston can be calculated using the formula:
Force = Pressure * Area

Since we know the pressure and the area of the small piston (0.0001 m^2), we can calculate the force:
Force on small piston = Pressure on small piston * Area of small piston

Step 4: Calculate the mass of the small piston (m).

The force exerted on the small piston is equal to the weight of the small piston's mass (m) multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, we can set up the equation:
Force on small piston = m * 9.8

Now we can substitute the force value from Step 3 into the equation and solve for m:
Force on small piston = m * 9.8
Force on small piston = (Pressure on small piston * Area of small piston) * 9.8

Solve the equation to find the mass (m) of the small piston:
m = (Force on small piston) / 9.8

By substituting the values calculated in previous steps, you can determine the value of m.