The load-bearing piston in a certain hydraulic system has an area 20 times as large as the input piston. If the larger piston supports a load of 2000N, how large a force must be applied to the input piston?
A certain boat displaces a volume of 4.5m3 of water (the density of the water is 1000kg/m3)
A- what is the mass of the water displaced by the boat?
b-What is the buoyant force acting on the boat?
the pressures F/A on both pistons should be equal. F = force, A = area
2000/20 = X/1
100 = X
______________
To find the force required to be applied to the input piston, we can use the principle of Pascal's Law. Pascal's Law states that the pressure applied to a fluid in a confined space is transmitted undiminished to all portions of the fluid and the container. In this case, we can equate the pressure on the larger piston (load-bearing piston) to the pressure on the smaller piston (input piston).
Let's assume the area of the input piston is A, and the area of the load-bearing piston is 20A.
According to Pascal's Law, the pressure on both pistons is the same.
So, we can set up the equation:
Force on the input piston / Area of the input piston = Force on the load-bearing piston / Area of the load-bearing piston
F_input / A = 2000N / (20A)
Simplifying the equation, we get:
F_input = (2000N / 20) * A
F_input = 100N * A
So, to find the force required to be applied to the input piston, we need to know the area of the input piston.
-----------------------------------------------------------------------------------------------------------------------
To find the mass of the water displaced by the boat, we can use the formula:
Mass = Density × Volume
Given that the density of water is 1000 kg/m^3 and the volume displaced by the boat is 4.5 m^3, we can substitute these values into the formula:
Mass = 1000 kg/m^3 × 4.5 m^3
Mass = 4500 kg
So, the mass of the water displaced by the boat is 4500 kg.
-----------------------------------------------------------------------------------------------------------------------
To calculate the buoyant force acting on the boat, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object (i.e., the mass of the fluid displaced multiplied by the acceleration due to gravity).
Using the same values as in the previous question (density of water = 1000 kg/m^3 and volume displaced by the boat = 4.5 m^3), we can find the mass of the water displaced:
Mass = Density × Volume = 1000 kg/m^3 × 4.5 m^3 = 4500 kg
The buoyant force is then calculated as:
Buoyant force = Mass × Acceleration due to gravity = 4500 kg × 9.8 m/s^2
Buoyant force = 44100 N
Therefore, the buoyant force acting on the boat is 44100 N.
To find the force that must be applied to the input piston in the hydraulic system, you need to apply Pascal's law, which states that pressure in a fluid is transmitted equally in all directions. The formula to calculate the force is:
Force = Pressure x Area
Given that the load-bearing piston has an area 20 times larger than the input piston, we can express it as:
Area of larger piston = 20 x Area of input piston
Let's assume the area of the input piston is A, and the area of the larger piston is 20A. The pressure is the same throughout the hydraulic system. The formula for pressure is:
Pressure = Force / Area
We can use this formula to set up an equation between the larger piston and the input piston:
Pressure of input piston = Pressure of larger piston
Force of input piston / Area of input piston = Force of larger piston / Area of larger piston
We are given that the force of the larger piston is 2000N and the area of the larger piston is 20A. Plugging in these values, we get:
Force of input piston / A = 2000N / (20A)
Simplifying the equation, we find:
Force of input piston = 2000N / 20
Therefore, the force that must be applied to the input piston is 100N.
For the boat question:
A) To find the mass of the water displaced by the boat, we can use the formula:
Mass = Density x Volume
Given that the density of water is 1000kg/m3 and the volume displaced by the boat is 4.5m3, we can substitute these values into the equation:
Mass = 1000kg/m3 x 4.5m3
Multiplying these numbers together, we find that the mass of the water displaced by the boat is 4500 kg.
B) The buoyant force acting on the boat is equal to the weight of the water displaced by the boat. So, we can calculate the buoyant force using the formula:
Buoyant force = Weight of water displaced
Weight of water displaced = Mass x Gravity
The acceleration due to gravity is approximately 9.8 m/s2. Plugging in the values, we have:
Buoyant force = 4500 kg x 9.8 m/s2
Multiplying these numbers together, we find that the buoyant force acting on the boat is 44100 N.