Classical Mechanics Answers

When there is a flow of charge q in an electric circuit containing a resistor R, capacitor C and inductor

L, there is a direct analogy with the moving parts of a mechanical oscillator comprising a mass m and a spring

with spring constant k. If a series LRC circuit is connected across a voltage source given by V = Vo cos ωt, the

flow of charge through the circuit is given by the following second order differential equation:

Lq¨+ Rq˙ +

1

C

q = V0 cos ωt.

(a) Determine the correspondence between the parameters of a driven mechanical oscillator (as discussed in

the notes) and the above driven electrical oscillator.

(b) Calculate the quality factor Q of the electrical circuit in terms of the coefficients of the above differential

equation.

(c) Show that, in the case of small or light damping, Q can be written as Q = R0/R, where R0 =

p

L/C is

the characteristic impedance of the circuit.

a bullet 2 cm long is fired at 420 m/s and passes straight through a 10 cm thick wooden-board, penetrate at 280 m/s . (a) what is the average acceleration of the bullet through the board? (b) what is the total time that the bullet is in contact with the board? (c) what minimum thickness could the board have if it was supposed the bullet?

define momentum

Suppose that the force on a 1kg mass on the surface of the earth is 10N and that the radius of the earth is about 600 km. Then the force on an 8kg mass placed at a point 2000 km from the center of the earth will be?