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
Gnom [1K]
3 years ago
5

The maximum speed of a mass m on an oscillating spring is vmax . what is the speed of the mass at the instant when the kinetic a

nd potential energy are equal?
Physics
1 answer:
umka21 [38]3 years ago
3 0
Let
A =  the amplitude of vibration
k =  the spring constant
m =  the mass of the object

The displacement at time, t, is of the form
x(t) = A cos(ωt)
where
ω =  the circular frequency.

The velocity is
v(t) = -ωA sin(ωt)

The maximum velocity occurs when the sin function is either 1 or -1.
Therefore
v_{max} = \omega A
Therefore
v(t) = -V_{max} sin(\omega t)

The KE (kinetic energy) is given by
KE = \frac{m}{2}v^{2} = \frac{m}{2} V_{max}^{2} sin^{2} (\omega t)

The PE (potential energy) is given by
PE = \frac{k}{2} x^{2} = \frac{k}{2} A^{2} cos^{2} (\omega t)

When the KE and PE are equal, then
v^{2} = \frac{k}{m} A^{2} cos^{2} (\omega t)

For the oscillating spring,
\omega ^{2} =  \frac{k}{m} \\ V_{max} = \omega A =  \sqrt{ \frac{k}{m} } A
Therefore
v^{2} =  \frac{k}{m}  \frac{m}{k} V_{max}^{2} cos^{2} ( \sqrt{ \frac{k}{m} t} ) \\ v = V_{max}  \,cos( \sqrt{ \frac{k}{m} t} )

Answer: v(t) = V_{max} cos( \sqrt{ \frac{k}{m} t} )

You might be interested in
Which of the following best describes the use of a renewable resource? (2 points) Most power plants burn fossil fuels to generat
kolbaska11 [484]

Which of the following best describes the use of a renewable resource?

Answer:

There are areas in California that use the heat from deep in the Earth to generate electricity.

Explanation:

It comes from the earth itself and we use a lot of things that comes from the earth and deep within it.

5 0
3 years ago
Which type of surface would most likely be the best reflector of electromagnetic energy?
Len [333]
<span>light colored and smooth surface would most likely be the best reflector of electromagnetic energy.Light, shiny surfaces are the best reflectors of radiation and they will allow the waves to reflect and bounce off rather than absorb. we can consider mirror as the example ,it will only reflect the light energy falling on them and it will not absorb. The darker coloured and rough surfaced substances will definitely absorb some amount of light falling on it. so light coloured smooth or shiny surfaced material would be the best reflector for electromagnetic energy.</span>
5 0
2 years ago
3.A bridge usually has expansion joints. They allow the bridge to become slightly longer when it
Dominik [7]

Answer:

a) When the sides of the joint are close together, the particles have more kinetic energy than they do when sides are farther apart.

Explanation:

5 0
3 years ago
How can you justifies the age of earth being 4.5 billion years old
IceJOKER [234]

Answer:

ummmmmmmmmm through science??

8 0
2 years ago
The movement of ocean water is caused by serveal processes______ results in the continual of ocean water facing in a global scal
34kurt

Answer:

A

Explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Which has a higher biotic potential, a pumpkin or a peach
    8·1 answer
  • The current limiting property of an inductor is called _____
    9·2 answers
  • The substances listed on the left side of a chemical equation are the _____.
    14·2 answers
  • The acceleration of an object would increase if there was an increase in the
    15·1 answer
  • At which of the above boundries is sea floor destroyed
    15·1 answer
  • How to do this question?​
    7·1 answer
  • U-235 releases an average of 2.5 neutrons per fission, while Pu-239 releases an average of 2.7 neutrons per fission. Which of th
    12·1 answer
  • NEED HELP PLEASE 15 POINTS PLEASEE NEED HELP
    13·2 answers
  • What defines a mixture?<br> for sience
    7·1 answer
  • Which of the following statements about electromagnetic radiation it true? A.electromagnetic waves with long wavelength are more
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!