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
lesya [120]
3 years ago
12

A flat solid disk of radius R and mass M is around vertical axle going through a center of mass of a disk. Suddenly a hoop of ma

ss M and radius R is falling coaxially on the disk. Hoop did not rotate initially. If rotational energy of the system was initially RE, what is rotational energy of the system after hoop has landed?
Physics
1 answer:
Softa [21]3 years ago
4 0

Answer:

Kf = 2/9 RE

Explanation:

The initial mechanical energy of the system is the sum of the kinetic and potential energy of the two bodies as the height does not change we can take the zero in the position of the disk, the ring is still so it has no energy and the energy disk is energy rotation kinetics

      K = ½ m₁ w₁²

In the final position the disc and the ring rotate together, so calluses contribute energy

      Kf = K₁ + K₂ = ½ (m₁ + m₂) w₂²

Where m1 is the mass of the disk, m2 the mass of the ring and w is the initial and final angular velocity

To find the final angular velocity, we treat the case as an inelastic shock, where the kinetic moment (L) is preserved, the system is formed by the two bodies.

       L₀ = Lf

       L₀ = I₁ w₁ + 0

       Lf = (I₁ + I₂) w₂

       I₁ w₁ = (I₁ + I₂) w ₂

       w₂ = I₁ / (I₁ + I₂) w₁

We take the kinetic moments of the bodies

Disk     I₁ = ½ m₁ R₁²

Hoop   I₂ = m₂ R₂²

Let's calculate the final angular velocity

     w₂ = ½ m₁ R² / (1/2 m₁ R² + m₂ R²) w₁

     w₂ = ½ m₁ / (m₁/2 + m₂) w₁

With this value we can substitute and calculate the final kinetic energy

     Kf = ½ (m₁ + m₂) [½ m₁ / (m₁ /2 + m₂) w₁]²  

     Kf = 1/8 [(m₁ + m₂) m₁² / (m₁/2 + m₂)²] w₁²

Let's substitute the values ​​that the mass and radius of the disc and ring give us are the same (M, R)

    Kf = 1/8 [2M M² / (3M/2)²] w₁² = ¼ M³ / (9M² /4) w₁²

    Kf = 1/9 M w₁²

This is the final kinetic energy, let's say it based on the initial (RE)

    Ko = RE = ½ M w₁²

    Kf / Ko = (1/9 M w₁²) / (1/2 M w₁²)

    Kf / RE = 2/9

    Kf = 2/9 RE

This loss of kinetic energy is transformed into internal energy during the crash

You might be interested in
A concave mirror has a radius of curvature of 0.60 meter.
love history [14]
Pls give me brainliest!!!
6 0
3 years ago
Heat transfers energy from a hot object to a cold object. Both objects are isolated from their surroundings. The change in entro
aniked [119]

To develop this problem we will start from the definition of entropy as a function of total heat, temperature. This definition is mathematically described as

S = \frac{Q}{T}

Here,

Q = Total Heat

T = Temperature

The total change of entropy from a cold object to a hot object is given by the relationship,

\Delta S = \frac{Q}{T_{cold}}-\frac{Q}{T_{hot}}

From this relationship we can realize that the change in entropy by the second law of thermodynamics will be positive. Therefore the temperature in the hot body will be higher than that of the cold body, this implies that this term will be smaller than the first, and in other words it would imply that the magnitude of the entropy 'of the hot body' will always be less than the entropy 'cold body'

Change in entropy \Delta S_{hot} is smaller than \Delta S_{cold}

Therefore the correct answer is C. Will always have a smaller magnitude than the change in entropy of the cold object

5 0
3 years ago
PLEASE HELP!
Kobotan [32]

Answer:

No

Explanation:

Cause a monster truck don

3 0
3 years ago
A comet is in an elliptical orbit around the sun. its closest approach to the sun is a distance of 4.5 1010 m (inside the orbit
barxatty [35]

r1 = 5*10^10 m , r2 = 6*10^12 m

v1 = 9*10^4 m/s

From conservation of energy

K1 +U1 = K2 +U2

0.5mv1^2 - GMm/r1 = 0.5mv2^2 - GMm/r2

0.5v1^2 - GM/r1 = 0.5v2^2 - GM/r2

M is mass of sun = 1.98*10^30 kg

G = 6.67*10^-11 N.m^2/kg^2

0.5*(9*10^4)^2 - (6.67*10^-11*1.98*10^30/(5*10^10)) = 0.5v2^2 - (6.67*10^-11*1.98*10^30/(6*10^12))

v2 = 5.35*10^4 m/s

4 0
3 years ago
The universal law of gravitation states that the force of attraction between two objects depends on which quantities?
Ronch [10]

Answer:

D. the masses of the objects and the distance between them

Explanation:

Gravitation is a force, a force doesn't care about the shape or density of objects, only about their masses... and distances.

And you can get it using the following equation:

f = \frac{Gm_{1}m_{2} }{d^{2} }

Where :

G is the universal gravitational constant : G = 6.6726 x 10-11N-m2/kg2

m represent the mass of each of the two objects

d is the distance between the centers of the objects.

4 0
3 years ago
Other questions:
  • Argon, neon, and xenon are examples of _________. A) halogens B) metalloids C) noble gases D) alkali metals
    13·2 answers
  • An ideal measuring device is one that does not alter the very measurement it is meant to take. Therefore, in comparison with the
    14·1 answer
  • A man stands on a scale in an elevator as shown here. the force of his weight when the elevator is still is fg downward. suppose
    7·1 answer
  • How much work, in N*m, is done when a 10.0 N force moves an object 2.5 m?
    9·1 answer
  • The circuit below shows some of the circuitry in a small toy robot. When the circuit is on the robot moves its arms, the motor,
    13·1 answer
  • A paper airplane is thrown horizontally with a velocity of 20 mph. The plane is in the air for 7.63 s before coming to a standst
    5·1 answer
  • A car is initially driving at 30 m/s. It hits a large pothole, after which it is traveling in the same direction but at 25 m/s.
    14·2 answers
  • 2. State law of conservation of
    15·1 answer
  • What is the acceleration of a car that starts from rest and achieves a speed of 45 m/s in 5 seconds?
    15·1 answer
  • 12,3,14,10,13,8 step 3 of 3 : determine if the data set is unimodal, bimodal, multimodal, or has no mode. identify the mode(s),
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!