Answer:
Use Fc centripetal force as positive and W the weight as negative
N = m v^2 / R + m g
v^2 = (N - m g) R / m
v^2 = (995 - 57 * 9.8) 42.7 / 57 = 327 m^2/s^2
v = 18.1 m/s
Note: N - m g is the net force producing the centripetal force
Answer:
A) 
B) 
C) 
D) mosquitoes speed in part B is very much larger than that of part C.
Explanation:
Given:
- Distance form the sound source,

- sound intensity level at the given location,

- diameter of the eardrum membrane in humans,

- We have the minimum detectable intensity to the human ears,

(A)
<u>Now the intensity of the sound at the given location is related mathematically as:</u>
..........................................(1)



<em>As we know :</em>


is the energy transferred to the eardrums per second.
(B)
mass of mosquito, 
<u>Now the velocity of mosquito for the same kinetic energy:</u>



(C)
Given:
- Sound intensity,

<u>Using eq. (1)</u>



Now, power:



Hence:




(D)
mosquitoes speed in part B is very much larger than that of part C.
Answer:
RL=100K → Vo=9.90 mV
RL=10K → Vo=9.09 mV
RL=1K → Vo=5 mV
RL=100 → Vo=909.09 μV
In order to obtain 80% of the power source we have to put a resistor of 4 KOhm.
Explanation:
Here we have a power source in serie with a resistor of 1K and RL, in order to obtain the Vo voltage we have to apply the voltage divider rule, that states:

Substituing the resistor values of RL we obtained the following results:
RL=100K → Vo=9.90 mV
RL=10K → Vo=9.09 mV
RL=1K → Vo=5 mV
RL=100 → Vo=909.09 μV
In order to find the lowest value that gives us 80% of the source voltage we have to use the voltage divider rule again and make the Vo equal to 0.8 Vin:

The result of the last equation is 4000, so in order to obtain 80% of the power source we have to put a resistor of 4 KOhm.