Hey!!
here is your answer>>>
Volaltage = It is the power to push the electrons
Capacitance = The ability to store electrical energy!.
Hope my answer helps!
Weight of the carriage ![=(m+M)g =142.1\ N](https://tex.z-dn.net/?f=%3D%28m%2BM%29g%20%3D142.1%5C%20N)
Normal force ![=Fsin(\theta) + W = 197.1\ N](https://tex.z-dn.net/?f=%3DFsin%28%5Ctheta%29%20%2B%20W%20%3D%20197.1%5C%20N)
Frictional force ![=\mu N=27.59\ N](https://tex.z-dn.net/?f=%3D%5Cmu%20N%3D27.59%5C%20N)
Acceleration ![=4.66\ m\ s^{-2}](https://tex.z-dn.net/?f=%3D4.66%5C%20m%5C%20s%5E%7B-2%7D)
Explanation:
We have to look into the FBD of the carriage.
Horizontal forces and Vertical forces separately.
To calculate Weight we know that both the mass of the baby and the carriage will be added.
- So Weight(W)
![=(m+M)\times g =(9.5+5)\ kg \times 9.8 =142.1\ Newton\ (N)](https://tex.z-dn.net/?f=%3D%28m%2BM%29%5Ctimes%20g%20%3D%289.5%2B5%29%5C%20kg%20%5Ctimes%209.8%20%3D142.1%5C%20Newton%5C%20%28N%29)
To calculate normal force we have to look upon the vertical component of forces, as Normal force is acting vertically.We have weight which is a downward force along with
, force of
acting vertically downward.Both are downward and Normal is upward so Normal force ![=Summation\ of\ both\ forces](https://tex.z-dn.net/?f=%3DSummation%5C%20of%5C%20both%5C%20forces)
- Normal force (N)
![= Fsin(\theta)+W=110sin(30) + 142.1 =197.1\ N](https://tex.z-dn.net/?f=%3D%20Fsin%28%5Ctheta%29%2BW%3D110sin%2830%29%20%2B%20142.1%20%3D197.1%5C%20N)
- Frictional force (f)
![=\mu N=0.14\times 197.1 =27.59\ N](https://tex.z-dn.net/?f=%3D%5Cmu%20N%3D0.14%5Ctimes%20197.1%20%3D27.59%5C%20N)
To calculate acceleration we will use Newtons second law.
That is Force is product of mass and acceleration.
We can see in the diagram that
and
component of forces.
So Fnet = Fy(Horizontal) - f(friction) ![= m\times a](https://tex.z-dn.net/?f=%3D%20m%5Ctimes%20a)
- Acceleration (a) =
![\frac{Fcos(\theta)-\mu N}{mass(m)} =\frac{(95.26-27.59)}{14.5}= 4.66\ m\ s{^2 }](https://tex.z-dn.net/?f=%5Cfrac%7BFcos%28%5Ctheta%29-%5Cmu%20N%7D%7Bmass%28m%29%7D%20%3D%5Cfrac%7B%2895.26-27.59%29%7D%7B14.5%7D%3D%204.66%5C%20m%5C%20s%7B%5E2%20%7D)
So we have the weight of the carriage, normal force,frictional force and acceleration.
Answer:
Thus the time taken is calculated as 387.69 years
Solution:
As per the question:
Half life of
= 28.5 yrs
Now,
To calculate the time, t in which the 99.99% of the release in the reactor:
By using the formula:
![\frac{N}{N_{o}} = (\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}](https://tex.z-dn.net/?f=%5Cfrac%7BN%7D%7BN_%7Bo%7D%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D)
where
N = No. of nuclei left after time t
= No. of nuclei initially started with
![\frac{N}{N_{o}} = 1\times 10^{- 4}](https://tex.z-dn.net/?f=%5Cfrac%7BN%7D%7BN_%7Bo%7D%7D%20%3D%201%5Ctimes%2010%5E%7B-%204%7D)
(Since, 100% - 99.99% = 0.01%)
Thus
![1\times 10^{- 4} = (\frac{1}{2})^{\frac{t}{28.5}}}](https://tex.z-dn.net/?f=1%5Ctimes%2010%5E%7B-%204%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B28.5%7D%7D%7D)
Taking log on both the sides:
![- 4 = \frac{t}{28.5}log\frac{1}{2}](https://tex.z-dn.net/?f=-%204%20%3D%20%5Cfrac%7Bt%7D%7B28.5%7Dlog%5Cfrac%7B1%7D%7B2%7D)
![t = \frac{-4\times 28.5}{log\frac{1}{2}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-4%5Ctimes%2028.5%7D%7Blog%5Cfrac%7B1%7D%7B2%7D%7D)
t = 387.69 yrs
To solve this problem it is necessary to use the concepts related to the Hall Effect and Drift velocity, that is, at the speed that an electron reaches due to a magnetic field.
The drift velocity is given by the equation:
![V_d = \frac{I}{nAq}](https://tex.z-dn.net/?f=V_d%20%3D%20%5Cfrac%7BI%7D%7BnAq%7D)
Where
I = current
n = Number of free electrons
A = Cross-Section Area
q = charge of proton
Our values are given by,
![I = 25 A](https://tex.z-dn.net/?f=I%20%3D%2025%20A)
![A= 1.2*20 *10^{-6} m^2](https://tex.z-dn.net/?f=A%3D%201.2%2A20%20%2A10%5E%7B-6%7D%20m%5E2)
![q= 1.6*10^{-19}C](https://tex.z-dn.net/?f=q%3D%201.6%2A10%5E%7B-19%7DC)
![N = 8.47*10^{19} mm^{-3}](https://tex.z-dn.net/?f=N%20%3D%208.47%2A10%5E%7B19%7D%20mm%5E%7B-3%7D)
![V_d =\frac{25}{(1.2*20 *10^{-6})(1.6*10^{-19})(8.47*10^{19} )}](https://tex.z-dn.net/?f=V_d%20%3D%5Cfrac%7B25%7D%7B%281.2%2A20%20%2A10%5E%7B-6%7D%29%281.6%2A10%5E%7B-19%7D%29%288.47%2A10%5E%7B19%7D%20%29%7D)
![V_d = 7.68*10^{-5}m/s](https://tex.z-dn.net/?f=V_d%20%3D%207.68%2A10%5E%7B-5%7Dm%2Fs)
The hall voltage is given by
![V=\frac{IB}{ned}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BIB%7D%7Bned%7D)
Where
B= Magnetic field
n = number of free electrons
d = distance
e = charge of electron
Then using the formula and replacing,
![V=\frac{(2.5)(25)}{(8.47*10^{28})(1.6*10^{-19})(1.2*10^{-3})}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B%282.5%29%2825%29%7D%7B%288.47%2A10%5E%7B28%7D%29%281.6%2A10%5E%7B-19%7D%29%281.2%2A10%5E%7B-3%7D%29%7D)
![V = 3.84*10^{-6}V](https://tex.z-dn.net/?f=V%20%3D%203.84%2A10%5E%7B-6%7DV)
Answer:
Explanation:
KE = ½mv² = ½(6.8)8² = 217.6 J
round as appropriate because that result is way too much precision for the inputs provided. Arguably should be 200 J based on the single significant digit of the velocity.