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Lagrangian and Hamiltonian's Mechanics

Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis, as shown in figure 7.17. Use cylindrical polar coordinates and let the equation of the parabola be z=kp^2. Write down the Lagrangian in terms of p as the

final temperature of iron-water system

A piece of iron of mass 200g at temperature 80 degrees C is added to a 300g of water at temp 10 degrees C. What is the final temperature of the system? [ The specific heat of water is 4190 J/(Kg . oC) and for iron is 450 J/(Kg . oC)]

Potential Energy - Angular Frequency

Please see attached file for formatted problem description. The potential energy of a one-dimensional mass m at a distance r from the origin is U(r) = U_o(r/R + lambda^2(R/r) for 0 < r < infinity, with U_o, R, and lambda all positive constants. Find the equilibrium position r_o. Let x be the distance from equilibrium an

One-Dimensional Spring

The force exerted by a one-dimensional spring, fixed at one end, is F=-kx, where x is the displacement of the other end from its equilibrium position. Assuming that this force is conservative (which it is) show that the corresponding potential energy is U=1/2kx^2, if we choose U to be zero at the equilibrium position. (b) Suppos

Capillary Rise: Determining the Rise of a Liquid in a Straw

Problem Statement: A double walled straw with an outer diameter of ½" and an inner diameter of ¼" is placed in a glass of water as shown and described below: a) Determine the volume of water in the 4" diameter by 4" high cup of water b) Determine how high the water will rise in both the outer layer of straw and the inne

Equilibrium: Contact force and tension in the ring.

Three identical steel balls, each of mass m, are placed in a cylindrical ring which rests on a horizontal surface and whose height is slightly greater than the radius of the balls. The diameter of the ring is such that the balls are virtually touching one another. A fourth identical ball is then placed on top of the other three

Equilibrium: Forcecs and Momements.

Please see attached. I am not sure if the mass of the block also needs to be taken into consideration- I would assume so, but no value is given?

Harmonic Motion

A person bounces up and down on a trampoline, while always staying in contact with it. The motion is simple harmonic motion, and it takes 1.98 s to complete one cycle. The height of each bounce above the equilibrium position is 54.0 cm. (a) Determine the amplitude of the motion. (b) Determine the angular frequency of the

MATLAB Solutions

Please see attached files regarding specifics. This problem has two parts (written & programming). The Brusselator is a simple model for oscillatory chemical systems such as the Belousov-Zhabotinski reaction. The time evolution of the concentration of two chemical species, x and y, is described by the ODE's: AND ,

Woman skating across ice lake

A 500 N woman stands in the middle of a frozen lake of radius lOOm. The ice is frictionless so she can't walk. She decides to sacrifice one of her 0.5 kg shoes and throws it horizontally at 5 m/s. How long does it take her to reach the shore?

Equilibrium, translational & rotational equilibrium

Please help with the following problem. Provide detailed calculations. A scale is attached to the ceiling and a mass of 1.00 kg hangs from it. It reads 9.81 N. Another identical scale at the right is connected by perfect strings passing over perfect pulleys to two 1.00 kg masses hanging vertically at the end of the strings (

Hookes Law: A massless spring and Morse function

1) A massless spring has unstretched length lo and force constant k. One end is now attached to the ceiling and a mass m is hung from the other. The equilibrium length of the spring is now l1. (a) Write down the condition that determines l1. Suppose now that the spring is stretched a further distance x beyond its new equilibri

Curvilinear One-Dimensional Systems

These problems are on curvilinear one dimensional systems and are giving me a lot of difficulty, if you could provide help along with visuals to help explain that would be very helpful. 1) Which of the following forces is conservative? (a) F = k (x, 2y, 3z) where k is constant. (b) F = k (y, x, 0). (c) F = k (-y, x, 0). For

Physics Lab - Static Equilibrium

Physics Lab experiment on Static Equilibrium: Laboratory data for this experiment has been provided. Do the data analysis and final conclusions. Draw the diagrams and show all equations used to understand. Also do questions at the end of the lab manual please.

Compressional force in the spine when a person bends forward to lift an object

Referring to the person is figure P12.51 on Page 384 in the text, determine the compressional force in the spine when the person bends forward to lift a 300 N object. The spine and upper body are represented as a uniform horizontal rod of weight 400 N. The erector spinalis muscle attaches at a point two thirds of the way up the

Harmonic oscillator and vibration

See attached files for full problem description. 1. In a physics lab, you attach a 0.200 kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. a) F

Spring Oscillations

A particle of mass ,m, is at rest at the end of a spring(force constant=k)hanging from a fixed support. At t=0 a constant downward forcd F is applied to the mass and acts for a time T. Show that after the force is removed, the displacement of the mass from its equilibrium position (x=Xe, where x is down) is: x - Xe =F

Normal force exerted by incline

A 2.00 kg block is held in equilibrium on an incline of angle = 70° by a horizontal force applied in the direction shown in Figure P4.50. If the coefficient of static friction between block and incline is µs = 0.300, determine the following (b) the normal force exerted by the incline on the block Your answer differs fro

Equilibrium of Forces

An unknown weight is placed on a string that is attached to two spring scales at a 60degree angle. The weight is evenly distributed and each spring scale reads 2.4 N. With this information and the conditions of static equilibrium, determine the weight of the unknown object. Please show all work. The same setup is used to me

1-D Quantum Mechanics with Atomic Ions

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. The figure below is a one-dimensional model of a crystal lattice. The ions have mass m, charge e, and an equilibrium separation b. a) Suppose the middle charge is d

Buoyant Force of a Helium Balloon

A helium filled balloon is attched to a 2 meter long, 0.050 kg string. The ballon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equillibrium, as in the attached picture. When deflated, the ballon has a mass of 0.25 kg. Determine the value of h.

Speed of wave in steel wire and tension in the wire.

A steel wire (8 m long and 60 g mass) is clamped between two parallel walls. Two equal masses are hung from the wire at equal distance from each end. The left and right sections of the wire are 2m long and make an angle of 40 degree with each wall and the middle section is 4 m long and is horizontal. A wave pulse travels along t

Standing waves

A 75 g bungee cord has an equilibrium length of 1.20 m. The cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This produces a standing wave with two antinodes. What is the spring constant (k) of the bungee cord?