Question

1) a) A block of mass m slides down an inclined plane starting from rest. If...

1)
a) A block of mass m slides down an inclined plane starting from
rest. If the surface is inclined an angle theta above the horizontal,
and the block reaches a speed V after covering a distance D along the
incline, what is the coefficient of kinetic friction?

b) at a distance D1 (still on the incline), the block comes to an
instantaneous standstill against a spring with spring constant k. How
far back up does the block? Why do we not worry about the impact of
static friction on the energy of the block?

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?

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