Classical mechanics is an extremely well tested model. Hundreds of years worth of experiments, as well as most feats of engineer
ing, have verified its validity. If special relativity gave very different predictions than classical physics in everyday situations, it would be directly contradicted by this mountain of evidence. In this problem, you will see how some of the usual laws of classical mechanics can be obtained from special relativity by simply assuming that the speeds involved are small compared to the speed of light.Two of the most surprising results of special relativity are time dilation and length contraction, namely, that measured intervals in time and space are not absolute quantities but instead appear differently to different observers. The equations for time dilation and length contraction can be written t=?t0 and l=l0/?, where?=11?u2c2?.Part AFind the first two terms of the binomial expansion for ?.Express your answer in terms of u and c.Hints? = 1+12(uc)2 … SubmitMy AnswersGive UpCorrectYou can see that ??1 if u?c, as is the case in most situations. If you set ?=1 in the equations for time dilation and length contraction you recover the equations of classical physics, which state essentially that there is no time dilation or length contraction. Therefore, we don't see any appreciable length contraction or time dilation in everyday life.Part BConsider a case involving a speed that is fast compared to those encountered in our everyday life: a spy plane moving at 1500m/s. Find the deviation from classical physics (??1) that relativity predicts at this speed. Use only the first two terms of the binomial expansion, as your calculator may not be able to handle the necessary number of digits otherwise.Express your answer to four significant figures.??1 = 1.250×10?11SubmitMy AnswersGive UpCorrectIf you lived for 70 years in such a spy plane moving at 1500m/s, this would amount to about 28ms of cumulative time difference between you and people who lived at rest relative to the earth when you finally landed. Thus, it is not surprising that relativistic effects are not observed in everyday life, or even at the fringes of everyday life. By using atomic clocks, which can measure time accurately to one part in 1013 or better, the time dilation at the normal speed for an airliner has been verified.Part CNow, consider the relativistic velocity addition formula:speed=v+u1+vuc2.If v=u=0.01c=1% of c, what is the relativistic sum of the two speeds?Express your answer as a percentage of the speed of light to five significant figures.
1 answer:
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1) Average speed
2) Displacement
Explanation:
1)
Speed is a scalar quantity which gives a measure of how fast a body is moving. It is equal to the ratio between the distance travelled by an object and the time taken to cover that distance:
where
d is the distance covered
is the time taken
It is important to note that being a scalar, speed does not have any direction. Moreover, distance is also a scalar quantity, which corresponds to the total length of the path covered by the object, regardless on the direction taken.
So, the equation "travelled distance/elapsed time" corresponds to the average speed. (where the term average refers to the fact we are not measuring the speed at a specific instant in time, but on a certain time interval .
2)
Velocity is a vector quantity, so it has both a magnitude and a direction.
The magnitude of the velocity is given by:
where
is the change in position (or displacement) of the object
is the time taken
And the direction of the velocity corresponds to the direction of the displacement.
We must note that while distance does not depend on the direction, displacement does. In fact, displacement measures the difference between the initial and final position of the object.
Therefore, the equation "change in position / elapsed time" is equal to the average velocity.
Learn more about speed and velocity:
brainly.com/question/8893949 (speed)
brainly.com/question/5063905 (speed vs velocity)
brainly.com/question/5248528 (velocity)
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Answer:
Approximately 1.62 × 10⁻⁴ V.
Explanation:
The average EMF in the coil is equal to
,
Why does this formula work?
By Faraday's Law of Induction, the EMF induced in a coil (one loop) is equal to the rate of change in the magnetic flux
through the coil.
.
Finding the average EMF in the coil is similar to finding the average velocity.
.
However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:
.
Hence the equation
.
Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in won't matter.
Apply this formula to this question. Note that , the magnetic flux through the coil, can be calculated with the equation
.
For this question,
is the strength of the magnetic field.
is the area of the coil.
is the number of loops in the coil.
is the angle between the field lines and the coil.
- At
, the field lines are parallel to the coil,
.
- At
, the field lines are perpendicular to the coil,
.
Initial flux: .
Final flux: .
Average EMF, which is the same as the average rate of change in flux:
.
Answer:
The trains will collide at a distance 1660 m from the station
Explanation:
Let the train traveling due north with a constant speed of 100 m/s be Train A.
Let the train traveling due south with a constant speed of 136 m/s be Train B.
From the question, Train B leaves a station 2,881 m away (that is 2,881 m away from Train A position).
Hence, the two trains would have traveled a total distance of 2,881 m by the time they collide.
∴ If train A has covered a distance m by the time of collision, then train B would have traveled
m.
Also,
At the position where the trains will collide, the two trains must have traveled for equal time, t.
That is, At the point of collision,
is the time spent by train A
is the time spent by train B
From,
Since the time spent by the two trains is equal,
Then,
m
m
m/s
m/s
Hence,
≅ 1,221 m
This is the distance covered by train A by the time of collision.
Hence, Train B would have covered (2881 - 1221)m = 1660 m
Train B would have covered 1660 m by the time of collision
Since it is train B that leaves a station,
∴ The trains will collide at a distance 1660 m from the station.