1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ket [755]
3 years ago
6

A uniform Rectangular Parallelepiped of mass m and edges a, b, and c is rotating with the constant angular velocity ω around an

axis which coincides with the parallelepiped’s large diagonal.
a. What is the parallelepiped’s kinetic energy?
b. What torque must be applied to the axis of rotation in order to keep it still? (neglect the gravity.)
Physics
1 answer:
Sonbull [250]3 years ago
8 0

Answer:

(a) k = \frac{Mw^{2} }{6} (a^{2} +b^{2} )

(b)  τ = \frac{M}{3} (a^{2} +b^{2} ) ∝

Explanation:

The moment of parallel pipe rotating about it's axis is given by the formula;

I = \frac{M}{3} (a^{2} +b^{2} )   ---------------------------------1

(a) The kinetic energy of a parallel pipe is also given as;

k =\frac{1}{2} Iw^{2} --------------------------------2

Putting equation 1 into equation 2, we have;

k = \frac{M}{6} (a^{2} +b^{2} )w^{2}

k = \frac{Mw^{2} }{6} (a^{2} +b^{2} )

(b) The angular momentum is given by the formula;

τ = Iw -----------------------3

Putting equation 1 into equation 3, we have

τ = \frac{Mw}{3} (a^{2} +b^{2} )

But

τ = dτ/dt = \frac{M}{3} (a^{2} +b^{2} )\frac{dw}{dt}   ------------------4

where

dw/dt = angular acceleration =∝

Equation 4 becomes;

τ = \frac{M}{3} (a^{2} +b^{2} ) ∝

You might be interested in
A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is
olga nikolaevna [1]

Explanation:

It is given that,

Spring constant of the spring, k = 15 N/m

Amplitude of the oscillation, A = 7.5 cm = 0.075 m

Number of oscillations, N = 31

Time, t = 15 s

(a) Let m is the mass of the ball. The frequency of oscillation of the spring is given by :

f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}

Total number of oscillation per unit time is called frequency of oscillation. Here, f=\dfrac{31}{15}=2.06\ Hz

m=\dfrac{k}{4\pi^2f^2}

m=\dfrac{15}{4\pi^2\times 2.06^2}

m = 0.0895 kg

or

m = 89 g

(b) The maximum speed of the ball that is given by :

v_{max}=A\times \omega

v_{max}=A\times 2\pi f

v_{max}=0.075\times 2\pi \times 2.06

v_{max}=0.970\ m/s

v_{max}=97\ cm/s

Hence, this is the required solution.

5 0
3 years ago
What does a biomass pyramid show?
lora16 [44]

Answer:

I SAVE D1K BY GIVING IT CPR

Explanation:

5 0
3 years ago
Read 2 more answers
When balancing an equation, you can
attashe74 [19]
D. write down the coefficients
7 0
3 years ago
A man who works for a moving company is loading a box onto a moving van. He pushes a 200N box up a 5m long ramp. If he pushes wi
OlgaM077 [116]

Answer:

η = 0.667 = 66.7%

Explanation:

The efficiency of the man can be given by the following formula:

η = output/input

where,

η = efficiency of man = ?

output = potential energy gain of the box = Wh

input = work done by man = Fd

Therefore,

\eta = \frac{Wh}{Fd}

where,

W = weight of box = 200 N

h = height gained by box = 1 m

F = force exerted by man = 60 N

d = length of ramp = 5 m

Therefore,

\eta = \frac{(200\ N)(1\ m)}{(60\ N)(5\ m)}

<u>η = 0.667 = 66.7%</u>

8 0
3 years ago
How does Newton describe the dependence of acceleration of a body on its mass and the net applied force?
tatiyna
<h2>Isaac Newton's First Law of Motion states, "A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force." What, then, happens to a body when an external force is applied to it? That situation is described by Newton's Second Law of Motion.  </h2><h2> equation as ∑F = ma </h2><h2> </h2><h2>The large Σ (the Greek letter sigma) represents the vector sum of all the forces, or the net force, acting on a body.  </h2><h2> </h2><h2>It is rather difficult to imagine applying a constant force to a body for an indefinite length of time. In most cases, forces can only be applied for a limited time, producing what is called impulse. For a massive body moving in an inertial reference frame without any other forces such as friction acting on it, a certain impulse will cause a certain change in its velocity. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity (unless, of course, the impulse causes the body to stop). </h2><h2> </h2><h2>There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth. In this case, the constant acceleration due to gravity is written as g, and Newton's Second Law becomes F = mg. Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down. </h2><h2> </h2><h2>The product of mass times gravitational acceleration, mg, is known as weight, which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force ma that is greater than the downward gravitational force mg.  </h2><h2> </h2><h2>Newton's second law in action </h2><h2>Rockets traveling through space encompass all three of Newton's laws of motion. </h2><h2> </h2><h2>If the rocket needs to slow down, speed up, or change direction, a force is used to give it a push, typically coming from the engine. The amount of the force and the location where it is providing the push can change either or both the speed (the magnitude part of acceleration) and direction. </h2><h2> </h2><h2>Now that we know how a massive body in an inertial reference frame behaves when it subjected to an outside force, such as how the engines creating the push maneuver the rocket, what happens to the body that is exerting that force? That situation is described by Newton’s Third Law of Motion.</h2><h2 />
4 0
3 years ago
Other questions:
  • Assessing and monitoring your fluid levels will help you optimize your car's _______.
    7·1 answer
  • If a freely falling rock were equipped with a speedometer, by how much would itd speed readings increase with each second if it
    6·1 answer
  • As a laudably skeptical physics student, you want to test Coulomb's law. For this purpose, you set up a measurement in which a p
    11·1 answer
  • What is the force on a 15.5 kg ball that is falling freely due to the pull of gravity
    14·1 answer
  • An ambulance driver traveling at 31.0 m/s (69.3 mph) honks his horn as he sees a motorist ahead on the highway traveling in the
    13·1 answer
  • Need help!!! A charge of 8.5 × 10–6 C is in an electric field that has a strength of 3.2 × 105 N/C. What is the electric force a
    7·2 answers
  • Carbon bums in the presence of oxygen to give carbon dioxide. Which chemical equation describes this reaction?
    14·1 answer
  • A baseball is hit high and far. Which of the following statements is true? At the highest point,
    6·1 answer
  • The slope of a distance-time graph will give
    13·1 answer
  • Un automovil transita por una curva en forma de U y recorre una distancia de 400m en 30s sin embargo su posición final está a so
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!