Question

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?

Answer #1

A block of mass m = 3.3 kg is on an inclined plane with
a coefficient of friction μ1 = 0.39, at an
initial height h = 0.53 m above the ground. The plane is
inclined at an angle θ = 44°. The block is then compressed
against a spring a distance Δx = 0.13 m from its
equilibrium point (the spring has a spring constant of
k1 = 35 N/m) and released. At the bottom of the
inclined plane...

1.A small block of mass 3.5 kg starting from rest slides down on
an incline plane of height 2.0 m, 40 degrees with respect to
horizontal (Fig. 2). The coefficient of kinetic friction between
the block and the incline plane is 0.25. At the end of the incline
plane, the block hits the top of a hemispherical mound of ice
(radius 1.0 m) , loses 75% of final kinetic energy (KE=0.5mv*v)
before the collision, then slide down on the surface...

A 1 kg block, starting from rest, slides down a 22 degree
inclined plane that is .55m tall. At the bottom, the 1 kg block
collides with a 3 kg block. The two blocks stick together and slide
.52 m on a friction less horizontal surface for .52 sec. What is
the speed of the 1kg block before it collides with the 3 kg block?
What is the acceleration of the 1kg block as it travels down the
inclined plane?...

A block of weight 3.8 N is launched up a 30 ∘ inclined plane of
length 2.45 m by a spring with spring constant 2.35 kN/m and
maximum compression 0.10 m . The coefficient of kinetic friction is
0.50.
-Does the block reach the top of the incline?
-If so, how much kinetic energy does it have there; if not, how
close to the top, along the incline, does it get?

1) A block is released from point A and it slides down an
incline (theta = 30 degrees) where the coefficient of kinetic
friction is 0.3. It goes 5m and hits a spring with a spring
constant k = 500 N/m. While it is being acted upon by the spring,
assume it is on a frictionless surface.
a) How far is the spring compressed?
b) How far does the block go up the plane on the rebound from
the spring?...

A block slides down an inclined plane, starting from rest and
being pushed with a constant acceleration of 5.25 m/s2 over a
distance of 18.0 cm. It then decelerates at a constant rate of 1.10
m/s2 (because of friction), until it again comes to rest. Find the
total time the block is in motion.

a 4.0 block starts from rest and slides down a plane
inclined at 60° horizonta l. The coefficient of kinetic friction
between the Surface and the block is 0.20. The work done by
friction on the block is?

A box with 10 kg of mass slides down an inclined plane that is
1.7 m high and 3.5 m long. Due to friction the box reaches 3.0 m/s
at the bottom of the inclined plane. Beyond the inclined plane lies
a spring with 650 N/m constant. It is fixed at its right end. The
level ground between the incline and the spring has no friction
The box compressed the spring, got pushed back towards the
incline by the spring....

A box with 11 kg of mass slides down an inclined plane that is
2.0 m high and 3.5 m long. Due to friction the box reaches 3.3 m/s
at the bottom of the inclined plane. Beyond the inclined plane lies
a spring with 650 N/m constant. It is fixed at its right end. The
level ground between the incline and the spring has no friction
The box compressed the spring, got pushed back towards the
incline by the spring....

A wooden block with mass 1.80 kg is placed against a compressed
spring at the bottom of a slope inclined at an angle of 34.0 ?
(point A). When the spring is released, it projects the block up
the incline. At point B, a distance of 6.00 m up the incline from
A, the block is moving up the incline at a speed of 6.45 m/s and is
no longer in contact with the spring. The coefficient of kinetic
friction...

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