Question

From this week's lab you learned that the change in
gravitational potential energy of a falling body can be captured
and stored as a rotational kinetic energy of a spinning disk. This
gave you the idea of a regenerative driver for an elevator in a
tall building. When an elevator goes down the corresponding change
in the gravitational potential energy of the elevator is
transformed into the rotational kinetic energy of a solid
disk-shape flywheel which can be extracted and used to lift up the
elevator when needed.

(a) You consider a flywheel in a solid disk geometry of radius
*R* = 0.85 *m* and thickness *t* = 26
* cm* made out of carbon fiber reinforced
polymer (CFRP) of mass density

Consider an elevator in a 35-story tall building driven by this flywheel. The floor-to-floor (vertical) distance is 3.7

(b) The elevator is used to transport down 3 identical heavy cargos from the floor number 26 to the floor number 4. Each cargo's mass is 841

Answer #1

**solution:** In this problem, we have to use the
principle of conservation of mechanical energy. follow the steps, I
have shown below.

QUESTION 27
A uniform disk of radius 0.40 m and mass 31.0 kg rolls on a
plane without slipping with angular speed 3.0 rad/s. The rotational
kinetic energy of the disk is __________. The moment of inertia of
the disk is given by 0.5MR2.

Plot the gravitational potential energy of a 2 kg ball as a
function of height above the floor, presuming the potential energy
is zero at the floor. If the ball has an initial velocity (at
height h=0) of 12 m/s, plot both the total energy and the kinetic
energy of the ball as a function of h. What is the maximum height
attained by the ball?

Please be detailed! Will rate!
An elevator carries a group of people from the ground floor to
the third floor of a building. The elevator and passengers have a
combined mass of 2600 kg. The height of one floor is 4.5 m. If the
elevator moves at a constant speed and goes from the ground floor
to the third floor in one minute, calculate the work done on the
elevator by gravity, the work done on the elevator by the...

A disk with mass m = 10.3 kg and radius R = 0.34 m begins at
rest and accelerates uniformly for t = 16.8 s, to a final angular
speed of ω = 26 rad/s.
1)
What is the angular acceleration of the disk?
rad/s2
2)
What is the angular displacement over the 16.8 s?
rad
3)
What is the moment of inertia of the disk?
kg-m2
4)
What is the change in rotational energy of the disk?
J
5)...

A ceiling fan consists of a small cylindrical disk with 5 thin
rods coming from the center. The disk has mass md = 3 kg
and radius R = 0.24 m. The rods each have mass mr = 1.2
kg and length L = 0.72 m.
1)
What is the moment of inertia of each rod about the axis of
rotation?
kg-m2
2)
What is the moment of inertia of the disk about the axis of
rotation?
kg-m2
3)
What...

A disk with mass m = 8.5 kg and radius R = 0.35 m begins at rest
and accelerates uniformly for t = 18.9 s, to a final angular speed
of ? = 29 rad/s.
a) What is the angular acceleration of the disk?
b) What is the angular displacement over the 18.9 s?
c) What is the moment of inertia of the disk?
d) What is the change in rotational energy of the disk?
e) What is the tangential...

To learn to use conservation of energy with the Newtonian form
for gravitational potential energy. Planet X, a planet with no
atmosphere, has a radius of 5.00×106 m and an unknown mass. You
drop an object from rest from a distance of 400 km above the
surface and find that it has a speed of 3010 m/s just before it
hits the ground.
Solve for the mass of planet X.

A ceiling fan consists of a small cylindrical disk with 5 thin
rods coming from the center. The disk has mass md = 2.6
kg and radius R = 0.24 m. The rods each have mass mr =
1.4 kg and length L = 0.78 m.
a) What is the moment of inertia of each rod about the axis of
rotation?
b) What is the moment of inertia of the disk about the axis of
rotation?
c) What is the...

A person with mass mp = 70 kg stands on a spinning
platform disk with a radius of R = 2.04 m and mass md =
186 kg. The disk is initially spinning at ω = 2 rad/s. The person
then walks 2/3 of the way toward the center of the disk (ending
0.68 m from the center).
What is the total moment of inertia of the system about the
center of the disk when the person stands on the...

A person with mass mp = 79 kg stands on a spinning
platform disk with a radius of R = 1.83 m and mass md =
183 kg. The disk is initially spinning at ω = 1.8 rad/s. The person
then walks 2/3 of the way toward the center of the disk (ending
0.61 m from the center).
1)
What is the total moment of inertia of the system about the
center of the disk when the person stands on...

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