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
ozzi
3 years ago
13

Two particles oscillate in simple harmonic motion along a common straight-line segment of length 1.0 m. Each particle has a peri

od of 1.5 s, but they differ in phase by π/6 rad.
(a) How far apart are they 0.45 s after the lagging particle leaves one end of the path?
(b) Are they then moving in the same direction, toward each other, or away from each other?
Physics
1 answer:
igor_vitrenko [27]3 years ago
6 0

Answer:

a) the particles are <em>0.217 m </em>apart

b) <em>the particles are moving in the same direction</em>.

Explanation:

a) The amplitude of the oscillations is A/2 and the period of each particle is

T = 1.5 s however, they differ by a phase of π/6 rad. Let the phase of the first particle be zero so that the phase of the second particle is π/6. So we can write the coordinates of each of the particles as,

x₁ = A/2 cos(ωt)

x₂ = A/2 cos(ωt + π/6)

we can write the angular frequency ω, as

ω = 2π / T

so,

x₁ = A/2 cos(2π / T)

x₂ = A/2 cos(2π / T + π/6)

Thus, the coordinates of the particles at t = 0.45 s are,

x₁ = A/2 cos((2π × 0.45) / 1.5)) = -0.155 A

x₂ = A/2 cos((2π × 0.45) / 1.5) + π/6) = -0.372 A

Their separation at that time is, therefore,

Δx = x₁ - x₂

    = -0.155 A + 0.372 A

    = 0.217 A

since A = 1 m

Thus,

<em>Δx  = 0.217 m</em>

<em></em>

<em></em>

b) In order to find their directions, we must take the derivatives at t = 0.45 s.

Therefore,

v₁ = dx₁ / dt

   = (-πA / T) sin(2πt / T)

   = -(π(1) / 1.5) sin(2π(0.45) / 1.5)

   = -1.99

and,

v₂ = dx₂ / dt

   = (-πA / T) sin((2πt / T) + π/6)

   = -(π(1) / 1.5) sin((2π(0.45) / 1.5) + π/6)

   = -1.40

Since both v₁ and v₂ are negative, this shows that <em>the particles are moving in the same direction</em>.

You might be interested in
A "biconvex" lens is one in which both surfaces of the lens bulge outwards. Suppose you had a biconvex lens with radii of curvat
Stolb23 [73]

Answer: f=150cm in water and f=60cm in air.

Explanation: Focal length is a measurement of how strong light is converged or diverged by a system. To find the variable, it can be used the formula:

\frac{1}{f} = (nglass - ni)(\frac{1}{R1} - \frac{1}{R2}).

nglass is the index of refraction of the glass;

ni is the index of refraction of the medium you want, water in this case;

R1 is the curvature through which light enters the lens;

R2 is the curvature of the surface which it exits the lens;

Substituting and calculating for water (nwater = 1.3):

\frac{1}{f} = (1.5 - 1.3)(\frac{1}{10} - \frac{1}{15})

\frac{1}{f} = 0.2(\frac{1}{30})

f = \frac{30}{0.2} = 150

For air (nair = 1):

\frac{1}{f} = (1.5 - 1)(\frac{1}{10} - \frac{1}{15})

f = \frac{30}{0.5} = 60

In water, the focal length of the lens is f = 150cm.

In air, f = 60cm.

5 0
3 years ago
Read 2 more answers
Write the function of gonads​
navik [9.2K]

Answer:

The gonads, the primary reproductive organs, are the testes in the male and the ovaries in the female. These organs are responsible for producing the sperm and ova, but they also secrete hormones and are considered to be endocrine glands.

7 0
3 years ago
If the same quantity of heat is added to both a 2-liter and a 4-liter container of water, the temperature change for water in th
VikaD [51]

Answer:

brainly.com/question/10966794

Explanation:

3 0
3 years ago
What is the longitud of the middle of Romano swamp
OverLord2011 [107]

Answer:

37 W 47 N

Explanation:

5 0
3 years ago
Badminton is only an individual sport<br><br> True<br> False<br><br> (This is gym)
Alekssandra [29.7K]

Answer:

false

Explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which of these is a type of telescope?
    5·2 answers
  • As shown in the figure below, Justin walks from the house to his truck on a windy day. He walks 20 m toward
    5·1 answer
  • Relationship between oceanography and cryosphere
    8·1 answer
  • How long did it take until all the starting material was gone?
    15·1 answer
  • Why is dark silicon currently necessary?
    12·1 answer
  • The full spectrum of light is what?
    5·1 answer
  • How does eating food produced locally benefit the environment?
    10·2 answers
  • Một chất điểm dao động điều hòa trên trục Ox với phương trình vận tốc là
    6·1 answer
  • When Momentum is conserved it is called ________ .​
    11·2 answers
  • The magnitude of the force associated with the gravitational field is constant and has a value f. A particle is launched from po
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!