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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

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

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

Steady State & Plotting Trajectories in MATLAB

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?

Description of Equilibrium

I need help with these two question on moments and equilibrium: 1. In the figure, a 6.00-m-long, uniform beam is hanging from a point 1.00 m to the right of its center. The beam weighs 140N and makes an angle of 30.0 degrees with the vertical. At the right-hand end of the beam a 100-N weight is hung; an unknown weight w hangs

Equilibrium of 3 force vectors

Given 3 force vectors as shown in part C (attached file). With the measured directions for the first and second quadrant forces, and the magnitude of the force measurement along the negative y direction, calculate the theoretical tensions in the cords that are in the first two quadrants (use the summation of x and y component

Potential Energy and Energy Conservation (Graph)

Please see attached file for the problem Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of a particle. Potential energy diagrams for a particle are useful in predicting the motion of that particle. These diagrams allow one to determine the direction of the force acting o

Free Body Diagrams of Forces

Please solve each problem step by step giving solutions please. SHOW every equation used and every step getting to the answer. Show substitutions, etc. Please give units. Look below for pages. Adult student learning from ya'll and so you can read what I need help with I cut and paste the questions cause some cannot read m

The problem requires calculation of pressure on the bottom of a barge.

1) A loaded flat bottom barge floats in fresh water. The bottom of the barge is 4.06m below the water line. When the barge is empty the barge's bottom is only 1.36m below the water line. What is the difference between the pressure on the bottom of the loaded barge and the pressure at the water line? Answer in Pascals. 2) I

Torque Problem

5. A crane of mass mc = 3400 kg supports a load of ml = 11300 kg as in Figure. The crane is pivoted with a frictionless pin at A and rests against a smooth support at B. Find the reaction forces at A and B.