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Consider a particle of mass m contrained to lie on the surface of a cone with it's vertex pointing down and half angle alpha.
a) write the equations of constraint.
b) employing cylindrical coordinates, (rho,phi,z) write the equations of motion and reduce them to an equivalent one degree of freedom problem using the radial coordinate rho as the independent variable.
c) sketch the effective potential identified from the equations of motion.
d) find the conditions for a circular orbit (rho=rhozero=constant, rhodot=o). And obtain the frequency of small oscillations about rhozero.
An Earth satellite has a speed of 28100 km/hr when it is at its perigee, 281 km above Earth's surface. Find the apogee distance
q1. a horizontal uniform bar of mass 2.6 kg and length 3.0 m is hung horizontally on two vertical strings. string 1 is
Using Newton's Version of Kepler's Third Law II Part A Pluto's moon Charon orbits Pluto every 6.4 days with a semimajor axis of 19,700 kilometers. Calculate the combined mass of Pluto and Charon. Express your answer using two significant figures. ..
A 0.25 m segment of wire lies along the x-axis and carries a current of 4.7 A in the negative x direction. What is the force (magnitude and direction) on the segment of wire
A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, then 1.0 km north, What was the bear's average speed
When the temperature of a thin silver [? = 19 × 10-6 (C°)-1] rod is increased, the length of the rod increases by 3.7 × 10-3 cm. By how much does the length of the gold rod increase
An object of mass 3m0 moves to the right at 0.8c. Calculate its momentum and energy
The battery of a pocket calculator has a voltage of 4.0 V and devilers a current of 0.29 mA. In one hour of operation How much charge flows in the circuit
a snowboarder has a mass of 70 kg and is being carried by a lift. The lift has a constant inclination of 30o, what power must the motor produce to achieve the task
An electric scooter has a battery capable of supplying 140 Wh of energy. If friction forces and other losses account for 60.0 percent of the energy usage, what altitude change can a rider achieve when driving in hilly terrain, if the rider and scoote..
Two ants race across a table 62.0 cm long. One travels at 4.69 cm/s and other at 3 cm/s. When the first one crosses the finish line, how far behind is second one? Reply in units of cm.
A ball is thrown horizontally from the top a of building 43.7 m high. The ball strikes the ground at a point 114 m from the base of the building. What would the initial velocity be
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