Answer:
15.7 m/s
Explanation:
The motion of the cannonball is a accelerated motion with constant acceleration g = 9.8 m/s^2 towards the ground (gravitational acceleration). Therefore, the velocity of the ball at time t is given by:
![v(t)=u + gt](https://tex.z-dn.net/?f=v%28t%29%3Du%20%2B%20gt)
where
u = 0 is the initial velocity
g = 9.8 m/s^2 is the acceleration
t is the time
If we substitute t=1.6 s into the equation, we find the final velocity of the cannonball:
![v(1.6 s)=0+(9.8 m/s^2)(1.6 s)=15.7 m/s](https://tex.z-dn.net/?f=v%281.6%20s%29%3D0%2B%289.8%20m%2Fs%5E2%29%281.6%20s%29%3D15.7%20m%2Fs)
Answer: The ice cube would float on top of the water and the rock would sink to the bottom.
Explanation: The ice cube has a smaller density than the rock which allows the ice cube to float but makes the rock sink to the bottom of the glass of water.
I will try to define the net problem, without the intermediate message between the message as:
<em>An air-filled toroidal solenoid has a mean radius of 15.5 cm and a cross-sectional area of 4.95 cm2 . When the current is 12.5 A , the energy stored is 0.390 J . </em>
<em>Part A: How many turns does the winding have?</em>
To solve the problem it is necessary to apply the concepts related to the storage of energy in an inductor and how it is possible to calculate from the inductance the number of turns of the system.
By definition we know that the energy stored in an inductor is given by,
![E = \frac{1}{2} LI^2](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20LI%5E2)
Where,
L = Inductance
I = Current
In this way, clearing the Inductance in the previously given equation we have to
![L = \frac{2E}{I}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B2E%7D%7BI%7D)
![L = \frac{2(0.39J)}{12.5A}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B2%280.39J%29%7D%7B12.5A%7D)
![L = 0.0624H](https://tex.z-dn.net/?f=L%20%3D%200.0624H)
In a system the inductance is given by
![L =\frac{\mu_0 N^2A}{l}](https://tex.z-dn.net/?f=L%20%3D%5Cfrac%7B%5Cmu_0%20N%5E2A%7D%7Bl%7D)
Where l represents the length, however as we deal with the perimeter of a circle we have,
![L =\frac{\mu_0 N^2A}{2\pi R}](https://tex.z-dn.net/?f=L%20%3D%5Cfrac%7B%5Cmu_0%20N%5E2A%7D%7B2%5Cpi%20R%7D)
Replacing our values we have
![(0.0624)=\frac{(4\pi*10^{-7})(N)^2(12.5)}{2\pi (15.5/2*10^{-3})^2}](https://tex.z-dn.net/?f=%280.0624%29%3D%5Cfrac%7B%284%5Cpi%2A10%5E%7B-7%7D%29%28N%29%5E2%2812.5%29%7D%7B2%5Cpi%20%2815.5%2F2%2A10%5E%7B-3%7D%29%5E2%7D)
Re-arrange to find N,
![N^2 = \frac{(0.0624)2\pi (15.5/2*10^{-3})}{(4\pi*10^{-7})(4.95*10^{-4})}](https://tex.z-dn.net/?f=N%5E2%20%3D%20%5Cfrac%7B%280.0624%292%5Cpi%20%2815.5%2F2%2A10%5E%7B-3%7D%29%7D%7B%284%5Cpi%2A10%5E%7B-7%7D%29%284.95%2A10%5E%7B-4%7D%29%7D)
![N^2 = 4884848.48](https://tex.z-dn.net/?f=N%5E2%20%3D%204884848.48)
![N = 2210.16\approx 2211 turns](https://tex.z-dn.net/?f=N%20%3D%202210.16%5Capprox%202211%20turns)
Therefore the winding have 2211turns
Answer:
Lenz’s law states that an induced magnetic field in a conductor opposes the applied flux through the conductor.
Explanation:
According to the Lenz's law, the direction of induced e.m.f is such that it generates a current which in turn produces a magnetic field that would oppose the change causing it.
In other words, the direction of any magnetic induction effect is such that it opposes the cause of the effect.
Therefore; an induced magnetic field in a conductor, opposes the applied flux through the conductor.
Period = 2 seconds.
frequency = 1/2 cycle/second = 1/2 Hz
If it falls twice every four seconds, then it falls once every two seconds, therefore one falling period is two seconds.
Hz is equal to cycles per second. So if it goes through one cycle per two seconds, then it goes through 1/2 cycle per one second.
Hope this helps!