理论物理作业1
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Homework 1
1. A pole OL rotates around a fixed point O with a uniform angular speed ω, pushing the ring C moving along the fixed steel wire AB. d is the vertical distance between point O and steel wire AB. As shown in Fig.1. Calculate the velocity and the acceleration of the ring C.
2. Consider the motion of a cannonball of mass
m
launched from a cannon with speed 0v and elevation angle α. Suppose that the force of air resistance acted on the cannonball is proportional to the velocity of cannonball while it is flying,R F mbv =−G G , and b is a constant. The situation is shown in Fig.2. Calculate the velocity and trajectory of the flying cannonball.
3. Consider the motion of a particle of mass m moving in space. Using the sphere coordinate (,,)ρθϕ, calculate
(a) The displacement x δ, y δand z δ.
(b) The generalized forces for the particle acted on by a force ˆˆˆx x y y z z F F e F e F e =++G . x x