A cylinder of radius R, length L and density pc floats in water with its axis...
A cylinder of radius R, length L and density pc floats in water with its axis oriented vertically. Let pw be the density of water and let y be the distance from the surface of the water to the top of the cylinder. Determine the differential equation describing this system and solve it. In you answer include the frequency of oscillation and the equilibrium position in terms of pc,pw, L and g.
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A cylinder of radius R, length L and density pc
floats in water with its axis...
A wooden cylinder 30.0 cm high floats vertically in a tub of water. The top of...
A wooden cylinder 30.0 cm high floats vertically in a tub of water. The top of the cylinder is 14.1 cm above the surface of the liquid. What is the density of the wood?
1. A cylinder of mass m, height h and radius r floats partially submerged in a...
1. A cylinder of mass m, height h and radius r floats partially submerged in a liquid of density ρ. One third of the height of the cylinder is above the surface of the water. Johnny pushes the cylinder down by a small distance x<h/3, then he releases it from rest. A) prove that the resulting motion of the cylinder is a simple harmonic motion. B) Find the period of the small oscillations in terms of the given quantities (m,r,h,ρ)
1. A cylinder of mass m, height h and radius r floats partially submerged in a...
1. A cylinder of mass m, height h and radius r floats partially submerged in a liquid of density ρ. One third of the height of the cylinder is above the surface of the water. Johnny pushes the cylinder down by a small distance x<h/3, then he releases it from rest. A) prove that the resulting motion of the cylinder is a simple harmonic motion. B) Find the period of the small oscillations in terms of the given quantities (m,r,h,ρ)...
A cylinder of length LL and density is floating in a large tank with water
A cylinder of length \(L\) and density \(\rho\) is floating in a large tank with water (with density \(\rho_{\mathrm{w}}\) ) and oil (with density \(\rho_{\mathrm{o}}\) ). The cylinder is initially at rest. It is then pushed downward slightly and released, such that it undergoes a vertical oscillatory motion around the initial position. Assume that the fluids are incompressible and inviscid. Throughout the motion, the cylinder is always partially in the water, and partially in the oil.(a) Express the acceleration of...
A right circular cylinder has radius R and length L. and a nonuniform volume charge density...
A right circular cylinder has radius R and length L. and a nonuniform volume charge density p(p). If the z axis is chosen to coincide with the axis of the cylinder, the charge density is p(p) - p{z2) = p(z, z) = .p_0 + beta_ z. This means that the charge density varies linearly along the length of the cylinder. Find the force on a point charge q placed at the center of the cylinder. (Adapted from Reitz. Milford, and...
A cylindrical cork of radius R and length L is floating in a liquid such that...
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed...
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin. Obtain an expression for the electric potential as a function of z. Sketch a graph of the electric potential as a function of distance z, for -2l < z < 2l.
An aluminum cylinder of radius 0.10 meter and length 1.0 meter is fully submerged in fresh...
An aluminum cylinder of radius 0.10 meter and length 1.0 meter is fully submerged in fresh water and supported by a vertical string attached to one end. The cylinder is motionless and vertically oriented. The density of aluminum is 2700 kg/m3 . a) Find the "net" force exerted by the water on the cylinder. (First consider top, bottom, and curved sides separately.) b) Find the tension in the supporting string. c) If the cylinder were gold instead of aluminum, would...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
9. A cardboard tube of radius R and length L has a uniform charge density σ...
9. A cardboard tube of radius R and length L has a uniform charge density σ on its surface. Find the potential at a point on the axis of the tube at a distance d from the center.
A right circular cylinder has radius R and length L. and a nonuniform volume charge density p(p). If the z axis is chosen to coincide with the axis of the cylinder, the charge density is p(p) - p{z2) = p(z, z) = .p_0 + beta_ z. This means that the charge density varies linearly along the length of the cylinder. Find the force on a point charge q placed at the center of the cylinder. (Adapted from Reitz. Milford, and...
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
9. A cardboard tube of radius R and length L has a uniform charge density σ on its surface. Find the potential at a point on the axis of the tube at a distance d from the center.
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