Final answer:
The force that reaches the large piston in a hydraulic press can be found using the principle of Pascal's law. The force is equal to the pressure on the small piston multiplied by the area of the large piston. By calculating the pressure on the small piston and multiplying it by the area of the large piston, we can determine the force that reaches the large piston.
Step-by-step explanation:
The force that reaches the large piston in a hydraulic press can be found using the principle of Pascal's law. According to Pascal's law, the pressure in a fluid is transmitted equally in all directions. In this case, the pressure exerted on the small piston is equal to the pressure exerted on the large piston.
To find the force on the large piston, we can use the equation:
Force = Pressure x Area
Given that the area of the small piston is 16 cm2 and the area of the large piston is 8 dm2, we can convert the units to be consistent.
1 dm = 10 cm, so 8 dm2 = 8 x 10 x 10 = 800 cm2.
Now, let's find the pressure exerted on the small piston. We can use the formula:
Pressure = Force / Area
The mass on the small piston is 20 kg. On Earth, the acceleration due to gravity is approximately 9.8 m/s2.
The weight of the mass can be calculated as:
Weight = mass x acceleration due to gravity = 20 kg x 9.8 m/s2 = 196 N.
Now we can find the pressure by dividing the weight by the area:
Pressure = 196 N / 16 cm2 = 12.25 N/cm2.
Since the pressure is transmitted equally to the large piston, the force on the large piston can be found by multiplying the pressure by the area:
Force = Pressure x Area = 12.25 N/cm2 x 800 cm2 = 9800 N.
Therefore, the force that reaches the large piston is 9800 N.