A , steel cylinder floats in mercury. The axis of the cylinder is perpendicular to the surface. What length of steel is above the surface
Length of steel cylinder above the surface is
The cylinder floats in the mercury bath. So, the net force on it is zero. Use the expression for buoyant force and gravitational force and equate them to calculate the length of the steel above the surface.
The expression for buoyant force is,
Here, is density of fluid is volume of the displaced fluid, and is acceleration due to gravity.
The following figure shows the situation.
Here, is the length of the cylinder above the surface.
The buoyant force on the cylinder submerged in Mercury is,
From Archimedes principle, the buoyant force acting an the steel cylinder is equal to weight of the cylinder submerged and it is expressed as follows:
Here, is volume of the cylinder.
Combine the above two equations.
The volume of the displaced fluid is,
Replaceby , by in and rearrange the expression for .
Substitute for, for ,
A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. When in equilibrium, what length of the cylinder is submerged?
The two --diameter cylinders in FIGURE , closed at one end, open at the other, are joined to form a single cylinder, then the air inside is removed.
A. How much force does the atmosphere exert on the flat end of each cylinder?
B. Suppose one cylinder is bolted to a sturdy ceiling. How many football players would need to hang from the lower cylinder to pull the two cylinders apart?
Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional tiltmeter, used for decades, consisted of two or more water-filled metal cans placed some distance apart and connected by a hose. FIGURE shows two such cans, each having a window to measure the water height. Suppose the cans are placed so that the water level in both is initially at the mark. A week later, the water level in can is at the mark.
A. Did can move up or down relative to can ? By what distance?
B. Where is the water level now in can ?
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