Question

2)
a) why does conservation of momentum only require 0 net external
forces and doesn't care about internal forces?

b) a stationary incendiary bomb explodes into 3 pieces with masses m1,
m2, m3. If right after the explosion (so ignore gravity) pieces one
and two have velocities (v1x,v1y) and (v2x, v2y), what is the velocity
of piece three? Why does this explosion not conserve mechanical
energy? How can you get an explosion that conserves mechanical energy?

3) A simple harmonic oscillator consists of a spring with stiffness
constant k attached to a block of mass m. At time t=0 , the spring is
extended by x0 from equilibrium and the block’s velocity is v0 (moving
towards equilibrium).

(a) If the displacement of the spring from equilibrium is given by
x(t) = Acos(wt + phi). Find the amplitude A, angular frequency w, and
phase factor phi.
(b) What is the period of the oscillator?
(c) What is the total mechanical energy of the oscillator?
(d) What is the kinetic energy and potential energy of the oscillator
at an arbitrary -A<x<A?

Answer 1

2. (a) Internal forces always exist in pair with equal in magnitude but opposite in direction and thus does not cause any motion of the object. So the conservation of momentum principle does not care the internal forces.

(b)

(c) In explosion chemical energy is converted into mechanical energy. Since this is an energy conversion process thus the principle of conservation of energy will not hold.

(d) If the explosion is due to the mechanical reason so that the forces are mechanical then the principle of conservation of energy holds.

Give thumbs up if you like!