Answer:
Centripetal acceleration.
Explanation:
Centripetal acceleration is a property of a body moving in a uniform circular path and it is directed radially towards the center of the circle in which body is rotating.
The force which causes this acceleration is centripetal force which is also directed towards the center of the circle and pulls the body towards its center.
It is calculated through following formula
![a=v^2/r](https://tex.z-dn.net/?f=a%3Dv%5E2%2Fr)
where v is velocity and r is the radius of the circle.
Answer:
a) 5 N b) 225 N c) 5 N
Explanation:
a) Per Coulomb's Law the repulsive force between 2 equal sign charges, is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them, acting along the line that joins the charges, as follows:
F₁₂ = K Q₁ Q₂ / r₁₂²
So, if we make Q1 = Q1/5, the net effect will be to reduce the force in the same factor, i.e. F₁₂ = 25 N / 5 = 5 N
b) If we reduce the distance, from r, to r/3, as the factor is squared, the net effect will be to increase the force in a factor equal to 3² = 9.
So, we will have F₁₂ = 9. 25 N = 225 N
c) If we make Q2 = 5Q2, the force would be increased 5 times, but if at the same , we increase the distance 5 times, as the factor is squared, the net factor will be 5/25 = 1/5, so we will have:
F₁₂ = 25 N .1/5 = 5 N
Explanation:
Given that,
The mean kinetic energy of the emitted electron, ![E=390\ keV=390\times 10^3\ eV](https://tex.z-dn.net/?f=E%3D390%5C%20keV%3D390%5Ctimes%2010%5E3%5C%20eV)
(a) The relation between the kinetic energy and the De Broglie wavelength is given by :
![\lambda=\dfrac{h}{\sqrt{2meE}}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7Bh%7D%7B%5Csqrt%7B2meE%7D%7D)
![\lambda=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-31}\times 1.6\times 10^{-19}\times 390\times 10^3}}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%5Ctimes%209.1%5Ctimes%2010%5E%7B-31%7D%5Ctimes%201.6%5Ctimes%2010%5E%7B-19%7D%5Ctimes%20390%5Ctimes%2010%5E3%7D%7D)
![\lambda=1.96\times 10^{-12}\ m](https://tex.z-dn.net/?f=%5Clambda%3D1.96%5Ctimes%2010%5E%7B-12%7D%5C%20m)
(b) According to Bragg's law,
![n\lambda=2d\ sin\theta](https://tex.z-dn.net/?f=n%5Clambda%3D2d%5C%20sin%5Ctheta)
n = 1
For nickel, ![d=0.092\times 10^{-9}\ m](https://tex.z-dn.net/?f=d%3D0.092%5Ctimes%2010%5E%7B-9%7D%5C%20m)
![\theta=sin^{-1}(\dfrac{\lambda}{2d})](https://tex.z-dn.net/?f=%5Ctheta%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B%5Clambda%7D%7B2d%7D%29)
![\theta=sin^{-1}(\dfrac{1.96\times 10^{-12}}{2\times 0.092\times 10^{-9}})](https://tex.z-dn.net/?f=%5Ctheta%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B1.96%5Ctimes%2010%5E%7B-12%7D%7D%7B2%5Ctimes%200.092%5Ctimes%2010%5E%7B-9%7D%7D%29)
![\theta=0.010^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D0.010%5E%7B%5Ccirc%7D)
As the angle made is very small, so such an electron is not useful in a Davisson-Germer type scattering experiment.
a. The disk starts at rest, so its angular displacement at time
is
![\theta=\dfrac\alpha2t^2](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cdfrac%5Calpha2t%5E2)
It rotates 44.5 rad in this time, so we have
![44.5\,\mathrm{rad}=\dfrac\alpha2(6.00\,\mathrm s)^2\implies\alpha=2.47\dfrac{\rm rad}{\mathrm s^2}](https://tex.z-dn.net/?f=44.5%5C%2C%5Cmathrm%7Brad%7D%3D%5Cdfrac%5Calpha2%286.00%5C%2C%5Cmathrm%20s%29%5E2%5Cimplies%5Calpha%3D2.47%5Cdfrac%7B%5Crm%20rad%7D%7B%5Cmathrm%20s%5E2%7D)
b. Since acceleration is constant, the average angular velocity is
![\omega_{\rm avg}=\dfrac{\omega_f+\omega_i}2=\dfrac{\omega_f}2](https://tex.z-dn.net/?f=%5Comega_%7B%5Crm%20avg%7D%3D%5Cdfrac%7B%5Comega_f%2B%5Comega_i%7D2%3D%5Cdfrac%7B%5Comega_f%7D2)
where
is the angular velocity achieved after 6.00 s. The velocity of the disk at time
is
![\omega=\alpha t](https://tex.z-dn.net/?f=%5Comega%3D%5Calpha%20t)
so we have
![\omega_f=\left(2.47\dfrac{\rm rad}{\mathrm s^2}\right)(6.00\,\mathrm s)=14.8\dfrac{\rm rad}{\rm s}](https://tex.z-dn.net/?f=%5Comega_f%3D%5Cleft%282.47%5Cdfrac%7B%5Crm%20rad%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%286.00%5C%2C%5Cmathrm%20s%29%3D14.8%5Cdfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D)
making the average velocity
![\omega_{\rm avg}=\dfrac{14.8\frac{\rm rad}{\rm s}}2=7.42\dfrac{\rm rad}{\rm s}](https://tex.z-dn.net/?f=%5Comega_%7B%5Crm%20avg%7D%3D%5Cdfrac%7B14.8%5Cfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D%7D2%3D7.42%5Cdfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D)
Another way to find the average velocity is to compute it directly via
![\omega_{\rm avg}=\dfrac{\Delta\theta}{\Delta t}=\dfrac{44.5\,\rm rad}{6.00\,\rm s}=7.42\dfrac{\rm rad}{\rm s}](https://tex.z-dn.net/?f=%5Comega_%7B%5Crm%20avg%7D%3D%5Cdfrac%7B%5CDelta%5Ctheta%7D%7B%5CDelta%20t%7D%3D%5Cdfrac%7B44.5%5C%2C%5Crm%20rad%7D%7B6.00%5C%2C%5Crm%20s%7D%3D7.42%5Cdfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D)
c. We already found this using the first method in part (b),
![\omega=14.8\dfrac{\rm rad}{\rm s}](https://tex.z-dn.net/?f=%5Comega%3D14.8%5Cdfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D)
d. We already know
![\theta=\dfrac\alpha2t^2](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cdfrac%5Calpha2t%5E2)
so this is just a matter of plugging in
. We get
![\theta=179\,\mathrm{rad}](https://tex.z-dn.net/?f=%5Ctheta%3D179%5C%2C%5Cmathrm%7Brad%7D)
Or to make things slightly more interesting, we could have taken the end of the first 6.00 s interval to be the start of the next 6.00 s interval, so that
![\theta=44.5\,\mathrm{rad}+\left(14.8\dfrac{\rm rad}{\rm s}\right)t+\dfrac\alpha2t^2](https://tex.z-dn.net/?f=%5Ctheta%3D44.5%5C%2C%5Cmathrm%7Brad%7D%2B%5Cleft%2814.8%5Cdfrac%7B%5Crm%20rad%7D%7B%5Crm%20s%7D%5Cright%29t%2B%5Cdfrac%5Calpha2t%5E2)
Then for
we would get the same
.
Answer:
2m/s²
Explanation:
velocity = displacement (distance in a specified direction /time