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The governor for an engine, consists of two balls, each of mass m, attached by light arms to sleeves on a rotating rod. The upper sleeve is fixed to the rod, and the lower one of mass M is free to move up and down. Assume the arms to be massless and the angular velocity w to be costant. Find the Lagrangian and Hamiltonian functions, and obtain Hamilton's equations of motion describing the system. Solve for the angle theta at which the arms would stop waving, and obtain the frequency of small oscillations about the steady value. shown in figure 5.5
The angular speed of the shaft of a car's engine is 329 rad/s. Find how many revolutions does it complete in 3.0 hours
John's mass is 91 kilogram, and Barbara's is 67 kilogram. He is standing on the x axis at xJ = +9.80 m, Determine how far and in which direction does their center of mass move as a result of the switch
what is the potential difference between the plates. A particular freely falling object requires 1.85 s to travel the last 31.0 m before it hits the ground. From what height above the ground did it fall.
An electric heater used to boil small amounts of water consistsof a 15-Ω coil that is immersed directly in the water. Itoperates from a 120-V socket. How much times is required for thsiheater to raise the temperature of 0.5 kg of water from 13degrees..
If the final angles are measured to have the values ?=10° and f= 8°, calculate the final speeds for the two pucks
A uniform meter stick is in static rotational equilibrium when a mass of 220 g is suspended from the 5.0-cm mark, What is the mass of the meter stick
A 15kg crate is moved along a horizontal floor by pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 200N and the crate slides a distance of 10m.
Compute the volume charge density of the atmosphere, assuming it to be uniform between 300 and 450 m. (Hint: You may neglect the curvature of the earth. Why?)
A 2.9 kg block is released from rest on a 45° inclined ramp. The block will lose energy to friction at a constant rate of 4 J/m as it slides down the ramp
A 1500-kg car moving east at 28.00m/s collides with a 1720 kg car moving south at 15 m/s and the two cars stick together.
Two balls, each with a mass of 0.890 kg, exert a gravitational force of 8.06 × 10-11 N on each other. How far apart are the balls
You are looking straight down on a magnetic compass that is lying flat on a table. A wire is stretched horizontally under the table, parallel to and a short distance below the compass needle.
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