Placing a tube, with a radius of .30 cm, vertically into a barrel with a radius of 21 cm it was found that when the barrel was filled with water and the tube filled to 12 m the barrel burst. Calculate the mass of water in the tube and the net force exerted by the water in the barrel on the lid just before rupture.
mass=density water*PI*radiustube^2 *height
force= masswater*g
I would also look at pressure, force/area
To calculate the mass of water in the tube, we need to determine the volume of water in the tube using its height and radius.
1. Calculate the volume of the tube:
The formula for the volume of a cylinder is V = πr^2h, where V represents volume, r is the radius, and h is the height.
V_tube = π * (0.003 m)^2 * 12 m
V_tube ≈ 1.027 × 10^(-3) m^3
2. Calculate the density of water:
The density of water is approximately 1000 kg/m^3.
3. Calculate the mass of water in the tube:
Mass_tube = density * volume
Mass_tube = 1000 kg/m^3 * 1.027 × 10^(-3) m^3
Mass_tube ≈ 1.027 kg
Now, let's calculate the net force exerted by the water in the barrel on the lid before rupture.
4. Calculate the weight of the water in the barrel:
The weight of an object is given by the equation F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. The weight is the force exerted by the mass.
Weight_barrel = Mass_barrel * g
To find the mass of the barrel, we need to determine its volume and density.
The formula for the volume of a barrel is V = πr^2h, where r is the radius (21 cm ≈ 0.21 m) and h is the height (12 m).
V_barrel = π * (0.21 m)^2 * 12 m
V_barrel ≈ 1.826 m^3
The density of water is approximately 1000 kg/m^3, assuming the barrel is filled with water.
Mass_barrel = density * volume
Mass_barrel = 1000 kg/m^3 * 1.826 m^3
Mass_barrel ≈ 1826 kg
Weight_barrel = Mass_barrel * g
Weight_barrel ≈ 1826 kg * 9.8 m/s^2
Weight_barrel ≈ 17908.8 N
5. Calculate the upward force exerted by the water in the barrel on the lid:
The upward force exerted by the water is equal to the weight of the water in the tube plus the weight of the remaining water in the barrel.
Force_upward = Weight_tube + Weight_remaining_water
Weight_tube = Mass_tube * g
Weight_tube ≈ 1.027 kg * 9.8 m/s^2
Weight_tube ≈ 10.06 N
Weight_remaining_water = Weight_barrel - Weight_tube
Weight_remaining_water ≈ 17908.8 N - 10.06 N
Weight_remaining_water ≈ 17898.74 N
Therefore, the mass of water in the tube is approximately 1.027 kg, and the net force exerted by the water in the barrel on the lid just before rupture is approximately 17898.74 N.