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

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?...

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 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...

A block with mass m = 14.6 kg slides down an inclined plane of
slope angle 15.8 ° with a constant velocity. It is then projected
up the same plane with an initial speed 4.35 m/s. How far up the
incline will the block move before coming to rest?

A block of mass 4.0Kg slides
down an incline plane of length 10 meters that makes an angle of 30
degrees with the horizontal. The coefficient of kinetic friction
between the block and the incline is 0.3. If the block is has an
initial speed of 2mis down the incline at the top of the incline,
then what is the speed at the bottom? Show calculations. Indicate
answer.
In the previous problem, what
was the gain in Kinetic Energy? Show...

A block with a mass of 2.5kg lies on a surface that is inclined
at an angle of, θ=22o, with the horizontal. The coefficient of
friction between the block and the surface of the incline is,
uk=0.20.
a) Apply Newton’s 2nd Law to determine the acceleration of the
block as it slides down the
surface. Answer
--> [±1.9m/s2]
b) Determine the magnitude of the velocity of the block at the
base of the inclined surface
if the block starts from rest...

2. A block slides down a plane inclined at 35o with
respect to the horizontal, with coefficient of kinetic friction
0.2. Find the ratio of the time taken to slide down the plane
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down the plane if it were frictionless.
3. A 20 kg block slides frictionlessly down an inclined plane
that is 2.8 m long and 1.2 m high. A person pushes up against the
block, parallel...

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