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Q1. A particle moves in a circular orbit in an attractive potential V(r). Expand Lagrangian to second order about equilibrium coordinates, r_0, phi = wt and find the condition for stability against small oscillations.
Q2. What is the force of gravity between two 1490 kg cars separated by the distance of 33 m on an interstate highway?
A bat in a cave emits a sound pulse and receives an echo 0.22 second later. Assuming that the speed of sound is 339 m/s, how far did the sound (the longitudinal wave) travel during this time.
What is tension in the wire
Determine magnitude of the force
A 3.10-m-long, 310 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 73.0 kg construction worker stands at the far end of the beam. What is the magnitude of torque abou..
What was the average acceleration throughout the trip
The George Washington bridge, that spans the Hudson River between New York and Jersey, is 4670 feet long and is made out of steel, How much does it expand in length between winter and summer.
A Norwich MCE student is involved in a crucial out of class experiment. He is in his dorm room 34 feet above an historic rock wall. Describe the final result and state any assumptions that you need to make. Would the final result be any different o..
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 60.0 degrees above the horizontal. The rocket is fired toward the ground 11.0-m high wall, which is located 27.0 m away. By how much does the rocket clear the top of the wa..
The centripetal and tangential accelerations are equal
A spaceship moves past you at speed v. You calculate the ship to be 364 m long, whereas an astronaut on the ship measures a length of 420 m. Find v.
What is inductance of the solenoid
A submarine dives 90.0 m at an angle of 8.0° below the horizontal. What are the horizontal and vertical components of submarine's displacement? (Imagine that upward and the direction of the submarine's horizontal motion is positive.)
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