Answer:
The angular velocity is
Explanation:
From the question we are told that
The mass of each astronauts is
The initial distance between the two astronauts
Generally the radius is mathematically represented as
The initial angular velocity is
The distance between the two astronauts after the rope is pulled is
Generally the radius is mathematically represented as
Generally from the law of angular momentum conservation we have that
Here is the initial moment of inertia of the first astronauts which is equal to the initial moment of inertia of the second astronauts So
Also is the initial angular velocity of the first astronauts which is equal to the initial angular velocity of the second astronauts So
Here is the final moment of inertia of the first astronauts which is equal to the final moment of inertia of the second astronauts So
Also is the final angular velocity of the first astronauts which is equal to the final angular velocity of the second astronauts So
So
=>
=>
=>
=>
To solve this problem we need to apply the corresponding sound intensity measured from the logarithmic scale. Since in the range of intensities that the human ear can detect without pain there are large differences in the number of figures used on a linear scale, it is usual to use a logarithmic scale. The unit most used in the logarithmic scale is the decibel yes described as
Where,
I = Acoustic intensity in linear scale
= Hearing threshold
The value in decibels is 17dB, then
Using properties of logarithms we have,
Therefore the factor that the intensity of the sound was
-- In combination with 610 Hz, the beat frequency is 4 Hz.
So the unknown frequency is either (610+4) = 614 Hz
or else (610-4) = 606 Hz.
In combination with 605 Hz, the beat frequency will be
either (614-605) = 9 Hz or else (606-605) = 1 Hz.
-- In actuality, when combined with the 605 Hz, the beat
frequency is too high to count accurately. That must be
the 9 Hz rather than the 1 Hz.
So the unknown is (605+9) = 614 Hz.
Answer:
E = 3456 J
Explanation:
The electrical energy expended in a resistor can be easily calculated by using the following formula:
where,
E = Energy Expended = ?
I = current through 5 ohm resistor = 2.4 A
R = Resistance = 5 ohms
P = Electrical Power = VI
Since,
V = IR (Ohm's Law)
Therefore,
P = (IR)(I) = I²R = (2.4 A)²(5 ohms) = 28.8 Watt
t = time taken = (2 min)(60 s/1 min) = 120 s
Therefore,
E = (28.8 Watt)(120 s)
<u>E = 3456 J</u>