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
Yuri [45]
3 years ago
7

A spherical shell is rolling without slipping at constant speed on a level floor. What percentage of the shell's total kinetic e

nergy is translational kinetic energy
Physics
1 answer:
IgorC [24]3 years ago
7 0

Answer:

41.667 per cent of the total kinetic energy is translational kinetic energy.

Explanation:

As the spherical shell is rolling without slipping at constant speed, the system can be considered as conservative due to the absence of non-conservative forces (i.e. drag, friction) and energy equation can be expressed only by the Principle of Energy Conservation, whose total energy is equal to the sum of rotational and translational kinetic energies. That is to say:

E = K_{t} + K_{r}

Where:

E - Total energy, measured in joules.

K_{r} - Rotational kinetic energy, measured in joules.

K_{t} - Translational kinetic energy, measured in joules.

The spherical shell can be considered as a rigid body, since there is no information of any deformation due to the motion. Then, rotational and translational components of kinetic energy are described by the following equations:

Rotational kinetic energy

K_{r} = \frac{1}{2}\cdot I_{g}\cdot \omega^{2}

Translational kinetic energy

K_{t} = \frac{1}{2}\cdot m \cdot R^{2}\cdot \omega^{2}

Where:

I_{g} - Moment of inertia of the spherical shell with respect to its center of mass, measured in kg\cdot m^{2}.

\omega - Angular speed of the spherical shell, measured in radians per second.

R - Radius of the spherical shell, measured in meters.

After replacing each component and simplifying algebraically, the total energy of the spherical shell is equal to:

E = \frac{1}{2}\cdot (I_{g} + m\cdot R^{2})\cdot \omega^{2}

In addition, the moment of inertia of a spherical shell is equal to:

I_{g} = \frac{2}{3}\cdot m\cdot R^{2}

Then, total energy is reduced to this expression:

E = \frac{5}{6}\cdot m \cdot R^{2}\cdot \omega^{2}

The fraction of the total kinetic energy that is translational in percentage is given by the following expression:

\%K_{t} = \frac{K_{t}}{E}\times 100\,\%

\%K_{t} = \frac{\frac{1}{2}\cdot m \cdot R^{2}\cdot \omega^{2} }{\frac{5}{6}\cdot m \cdot R^{2}\cdot \omega^{2} } \times 100\,\%

\%K_{t} = \frac{5}{12}\times 100\,\%

\%K_{t} = 41.667\,\%

41.667 per cent of the total kinetic energy is translational kinetic energy.

You might be interested in
Can someone help me :)
zhenek [66]

Answer:

undergone a chemical change

Explanation:

6 0
3 years ago
Read 2 more answers
A bird accelerating from rest at a constant rate,experiences a displacement of 28 m in 11s.What is its acceleration
Ksenya-84 [330]
Use the formula below for this question:

v_{f} = v_{i} + 2 * a * d

re-arrange to solve for a:

a = \frac{v_{f} - v_{i}}{2 * d}

now simply plug in your variables and there's your answer :). If you ever get stuck, you can look up the kinematic equations!
4 0
3 years ago
1. A kangaroo hops 84 m to the east in 7 seconds.
DENIUS [597]

Explanation:

Given parameters:

Distance hopped  = 84m

Displacement  = 84m due east

Time  = 7s

Unknown:

Speed of kangaroo  = ?

Velocity of kangaroo  = ?

Solution:

To solve this problem,

    Speed  = \frac{distance}{time }   = \frac{84}{7}  = 12m/s

  Velocity  = \frac{displacement}{time}   = \frac{84}{7}   = 12m/s due east

3 0
3 years ago
Why is the process of photosynthesis important to food webs?
Slav-nsk [51]

Answer:

to know what that specif animal or thing does in the food chain

Explanation:

5 0
3 years ago
Based on the law of conservation of energy, how can we reasonably improve a machine’s ability to do work?
kifflom [539]
Based on the law of conservation of energy, we know that we can't create energy, machines can only convert one type of energy into another. So, if we want to improve a machines's ability then we need to reduce it's loss energy (part of energy which is useless). Out of all the options only Option C fits best with it.

In short, Your Answer would be Option C

Hope this helps!
6 0
3 years ago
Read 2 more answers
Other questions:
  • A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass 0.180 kg. The free end of the stri
    12·2 answers
  • Kevin can text 44 words in 8 minutes. At this rate, how many minutes would it take
    15·1 answer
  • Plz answer this asap first answer gets brainliest and 100 points
    12·2 answers
  • An electron moving with a velocity = 5.0 × 107 m/s enters a region of space where perpendicular electric and a magnetic fields a
    5·1 answer
  • You drive on Interstate 10 from San Antonio to Houston, half the time at 51 km/h and the other half at 71 km/h. On the way back
    7·1 answer
  • A 1100 kgkg safe is 2.4 mm above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compres
    10·1 answer
  • Someone pls help! My physics quiz is today:(
    11·2 answers
  • Correct unit of speed
    11·2 answers
  • If the magnification produced by a lens has a negative value, the image will be
    5·2 answers
  • Why do you think lightning is so dangerous if it strikes a person?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!