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)
Homework Answers
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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...
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)...
Help please step by step 3points each hents: (1 1. A cylinder of density pe and...
Help please step by step
3points each hents: (1 1. A cylinder of density pe and height h floats in a liquid of density ρ with half of its volume submerged into the liquid. Johnny removes the cylinder from equilibrium by puling it up a distance xch/2 and then he releases the cylinder from rest. A) prove that the motion of the cylinder after the release is simple harmonic motion b) find the period of the small oscillations as a...
(58%) Problem 1: The following diagrams snow pictures or Docks that are Toating partially submerged in...
(58%) Problem 1: The following diagrams snow pictures or Docks that are Toating partially submerged in a liquid. The mass and total volume or each of the blocks is given below each of the diagrams. m = 20 g V = 30 cm m = 40 g V. = 55 cm m, = 40 g V. = 80 cm m = 12 g V = 24 cm m = 20 g V. = 30 cm m = 60 g V....
A thin disk (radius R and mass M) attached to the top of a hollow cylinder (height & radius R and mass M) is wobbling while spinning. ←R-height-radius Derive an expression for the angular momentu...
A thin disk (radius R and mass M) attached to the top of a hollow cylinder (height & radius R and mass M) is wobbling while spinning. ←R-height-radius Derive an expression for the angular momentum L of the object lif its initial rotation vector ω ω|êut ω3ез. Assume that ω3 is large and nonzero, that ω! İs nonzero but small, and that ω2 is initially zero
A thin disk (radius R and mass M) attached to the top of a...
4. Find the total charge of a solid cylinder of height H and radius R. The...
4. Find the total charge of a solid cylinder of height H and radius R. The charge density of the cylinder is given by p k, where k is a constant.
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in...
question (c), (d), (e), (f) please. Thanks.
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
A non-uniform cylinder of mass M, Radius r and moment of Inertia Iem = 2 Mr2...
A non-uniform cylinder of mass M, Radius r and moment of Inertia Iem = 2 Mr2 is rolling on a roller coaster. It starts at rest at a height 2h above the ground. It travels downwards to a trough at height below the ground level with a speed of vi before climbing a hill of height with a speed of vh. Find v and Vh. Placed on top of the second hill is a loop of unknown radius R. Find...
A solid cylinder of mass m and radius r is at rest precariously at the top...
A solid cylinder of mass m and radius r is at rest precariously at the top of a hemispherical dome with radius R. The cylinder is then tipped and rolls down the dome with negligible friction. a) Find the height that the cylinder loses contact with the hemisphere.
The Figure below shows a homogeneous cylinder of radius R and mass m. Assuming that the...
The Figure below shows a homogeneous cylinder of radius R and mass m. Assuming that the cylinder rolls on a rough surface without sliding, derive the equations of motion using the energy conservation approach, and determine the natural frequency. 179
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls...
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.504 m from the end of the ramp. The initial height of the object is H = 0.88 m; the end of the ramp is at height h = 0.13 m. The object consists of an...
Help please step by step
3points each hents: (1 1. A cylinder of density pe and height h floats in a liquid of density ρ with half of its volume submerged into the liquid. Johnny removes the cylinder from equilibrium by puling it up a distance xch/2 and then he releases the cylinder from rest. A) prove that the motion of the cylinder after the release is simple harmonic motion b) find the period of the small oscillations as a...
(58%) Problem 1: The following diagrams snow pictures or Docks that are Toating partially submerged in a liquid. The mass and total volume or each of the blocks is given below each of the diagrams. m = 20 g V = 30 cm m = 40 g V. = 55 cm m, = 40 g V. = 80 cm m = 12 g V = 24 cm m = 20 g V. = 30 cm m = 60 g V....
A thin disk (radius R and mass M) attached to the top of a hollow cylinder (height & radius R and mass M) is wobbling while spinning. ←R-height-radius Derive an expression for the angular momentum L of the object lif its initial rotation vector ω ω|êut ω3ез. Assume that ω3 is large and nonzero, that ω! İs nonzero but small, and that ω2 is initially zero
A thin disk (radius R and mass M) attached to the top of a...
4. Find the total charge of a solid cylinder of height H and radius R. The charge density of the cylinder is given by p k, where k is a constant.
question (c), (d), (e), (f) please. Thanks.
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
A non-uniform cylinder of mass M, Radius r and moment of Inertia Iem = 2 Mr2 is rolling on a roller coaster. It starts at rest at a height 2h above the ground. It travels downwards to a trough at height below the ground level with a speed of vi before climbing a hill of height with a speed of vh. Find v and Vh. Placed on top of the second hill is a loop of unknown radius R. Find...
A solid cylinder of mass m and radius r is at rest precariously at the top of a hemispherical dome with radius R. The cylinder is then tipped and rolls down the dome with negligible friction. a) Find the height that the cylinder loses contact with the hemisphere.
The Figure below shows a homogeneous cylinder of radius R and mass m. Assuming that the cylinder rolls on a rough surface without sliding, derive the equations of motion using the energy conservation approach, and determine the natural frequency. 179
Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.504 m from the end of the ramp. The initial height of the object is H = 0.88 m; the end of the ramp is at height h = 0.13 m. The object consists of an...
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