For a system,the cylinder on the left,at L,has a mass of 600kg and a cross-sectional area of 800centi meter squad.The piston on the right,at S,has cross-sectional area 25centi meter squad abd negligible weight.If the apparatus is filled with oil(DENSITY=0.78grams/centi meter cube),find the force F required to hold the system in equilibrium.
1.15*10^5
To find the force required to hold the system in equilibrium, we need to consider the pressure exerted by the oil on each cylinder.
The pressure exerted by a fluid (in this case, oil) can be calculated using the formula:
Pressure = Force / Area
Let's calculate the pressure exerted by the oil on each cylinder:
For the left cylinder at L:
The mass of the cylinder (m) = 600 kg
Cross-sectional area of the cylinder (A) = 800 cm^2 = 800 * 10^-4 m^2
Density of the oil (ρ) = 0.78 g/cm^3 = 0.78 * 10^3 kg/m^3
The force (F_L) exerted by the oil on the left cylinder is equal to the weight of the cylinder:
F_L = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
For the right cylinder at S:
Cross-sectional area of the cylinder (A) = 25 cm^2 = 25 * 10^-4 m^2
The force (F_S) exerted by the oil on the right cylinder can be calculated using the formula:
F_S = P * A
where P is the pressure exerted by the oil on the right cylinder.
Since the system is in equilibrium, the force exerted by the oil on the left cylinder (F_L) is equal to the force exerted by the oil on the right cylinder (F_S). Therefore:
F_L = F_S
Now let's calculate the forces:
F_L = m * g = 600 kg * 9.8 m/s^2
To calculate the pressure exerted by the oil on the right cylinder (P), we need to find the density of the oil in kg/m^3:
Density = Mass / Volume
0.78 g/cm^3 = Mass / Volume
Mass = 0.78 g/cm^3 * Volume
Since Volume = Area * Height, and the height is the same for both cylinders, we can write the equation:
0.78 * 10^3 kg/m^3 = (0.78 g/cm^3 * 10^-4 m^2) * H
where H is the height of the oil column between the cylinders.
Now substitute the values in the equation:
P = (0.78 * 10^3 kg/m^3) * (0.78 g/cm^3 * 10^-4 m^2) * H
Now equating the forces:
m * g = P * A
600 kg * 9.8 m/s^2 = (0.78 * 10^3 kg/m^3) * (0.78 g/cm^3 * 10^-4 m^2) * H * A
Substituting the values of A for both cylinders:
600 kg * 9.8 m/s^2 = (0.78 * 10^3 kg/m^3) * (0.78 g/cm^3 * 10^-4 m^2) * H * (800 * 10^-4 m^2)
Solving the equation will give you the height (H) of the oil column, and hence the required force (F) to hold the system in equilibrium.