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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. 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 generalized coordinate. Find the equation of motion of the bead and determine whether there are positions of equilibrium, that is, values of p at which the bead can remain fixed, without sliding up or down the spinning wire. Discuss the stability of any equilibrium position you find.
An unstrained horizontal spring has a length of 0.37 m and a spring constant of 340 N/m. Two small charged objects are attached to this spring, one at each end. The charges on the objects have equal magnitudes.
An object is released from rest when it is a height habove the surface of a planet of mass M and radiusR. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance.
(a) Calculate the index of refraction of the polymer if the refracted angle is 26 degrees. (b) Calculate the critical angle of the polymer in air. (c) Calculate the speed of light in the polymer.
Small charged sphere, mass m = 1.2 x 10-4 kg and charge q = 3.2 nC is suspended (floating) a very small distance above a very large sheet charge due to electrostatic forces. What is the charge density (charge per area) of the sheet essential for this..
the rear window of a van is coated with a layer of ice at 0degc. the density of ice is 917 kgm3 and the latent heat of
1. Why does the final electron energy not depend on the grid voltage?
Tarzan swings on a 22.8 m long vineinitially inclined at an angle of 22° from the vertical. What is his speed at the bottom of theswing if he starts from rest
A point charge q1 = -2.3 x 10^ -6 C is located at the origin of a co-ordinate system. Another point charge q2 = 6.3 x 10^-6 C is located along the x-axis at a distance x2 = 6.1 cm from q1. 1) What is F12,x, the value of the x-component of the forc..
Estimate the linear separation of two objects on the planet Mars that can just be resolved under ideal conditions by an observer on Earth who is:
A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are 56.1° and 48.5°, respectively
A disk of mass M and radius R spins on a horizontal axis during its center. Particle, mass m, is on the rim at the top. When it now starts to spin what is disks (a) angular speed at m's lowest point (b) force exerted with disk on m
Sketch a free-body diagram of the plank. How far can a painter of mass 70.0 kg walk on the overhanging part of the plank before it tips.
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