A cross-country runner accelerates from 4 m/s to 7 m/s over the course of 5 seconds. What is the runner's average rate of accele
1 answer:
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Answer:
Explanation:
The <u>Heisenberg uncertainty principle</u> postulates that the fact each particle has a wave associated with it, imposes restrictions on the ability to determine its position and speed at the same time.
In other words:
It is impossible to measure simultaneously (according to quantum physics), and with absolute precision, the value of the position and the momentum (linear momentum) of a particle. Thus, in general, the greater the precision in the measurement of one of these magnitudes, the greater the uncertainty in the measure of the other complementary variable.
Mathematically this principle is written as:
(1)
Where:
is the uncertainty in the position of the electron
is the Planck constant
is the mass of the electron
is the uncertainty in the velocity of the electron.
If we know the accuracy of the velocity is of the velocity of the electron
, then
is:
(2)
Now, the least possible uncertainty in position is:
(3)
(4)
Finally:
A) Angular speed: 0.42 rev/s
B) Frequency: 0.42 Hz
C) Tangential speed: 26.4 cm/s
D) Distance travelled: 528 cm
Explanation:
A)
In this problem, the ladybug is rotating together with the record.
The angular velocity of the ladybug, which is defined as the rate of change of the angular position of the ladybug, in this problem is
where here it is measured in revolutions per minute.
Keeping in mind that
1 minute = 60 seconds
We can rewrite the angular speed in revolutions per second:
B)
The relationship between angular speed and frequency of revolution for a rotational motion is given by the equation
(1)
where
is the angular speed
f is the frequency of revolution
For the ladybug in this problem,
Keeping in mind that , the angular speed can be rewritten as
And re-arranginf eq.(1), we can find the frequency:
And the frequency is the number of complete revolutions made per second.
C)
For an object in circular motion, the tangential speed is related to the angular speed by the equation
where
is the angular speed
v is the tangential speed
r is the distance of the object from the axis of rotation
For the ladybug here,
is the angular speed
r = 10 cm = 0.10 m is the distance from the center of the record
So, its tangential speed is
D)
The tangential speed of the ladybug in this motion is constant (because the angular speed is also constant), so we can find the distance travelled using the equation for uniform motion:
where
v is the tangential speed
t is the time elapsed
Here we have:
v = 26.4 cm/s (tangential speed)
t = 20 s
Therefoe, the distance covered by the ladybug is
Learn more about circular motion:
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