The De Broglie's wavelength of a particle is given by:
![\lambda=\frac{h}{p}](https://tex.z-dn.net/?f=%20%5Clambda%3D%5Cfrac%7Bh%7D%7Bp%7D%20%20)
where
is the Planck constant
p is the momentum of the particle
In this problem, the momentum of the electron is equal to the product between its mass and its speed:
![p=m_e v=(9.1 \cdot 10^{-31} kg)(7.0 \cdot 10^7 m/s)=6.4 \cdot 10^{-23} kg m/s](https://tex.z-dn.net/?f=%20p%3Dm_e%20v%3D%289.1%20%5Ccdot%2010%5E%7B-31%7D%20kg%29%287.0%20%5Ccdot%2010%5E7%20m%2Fs%29%3D6.4%20%5Ccdot%2010%5E%7B-23%7D%20kg%20m%2Fs%20)
and if we substitute this into the previous equation, we find the De Broglie wavelength of the electron:
![\lambda=\frac{h}{p}=\frac{6.6 \cdot 10^{-34} Js}{6.4 \cdot 10^{-23} kg m/s}=1.0 \cdot 10^{-11} m](https://tex.z-dn.net/?f=%20%5Clambda%3D%5Cfrac%7Bh%7D%7Bp%7D%3D%5Cfrac%7B6.6%20%5Ccdot%2010%5E%7B-34%7D%20Js%7D%7B6.4%20%5Ccdot%2010%5E%7B-23%7D%20kg%20m%2Fs%7D%3D1.0%20%5Ccdot%2010%5E%7B-11%7D%20m%20%20%20)
So, the answer is True.
Answer:
When we double the angular velocity the maximum acceleration
will changes by a factor of 4.
Explanation:
Given the angular frequency
of the simple harmonic oscillator is doubled.
We need to find the change in the maximum acceleration of the oscillator.
![a_{max}=A\omega^2](https://tex.z-dn.net/?f=a_%7Bmax%7D%3DA%5Comega%5E2)
Now, according to the problem, the angular frequency
got doubled.
Let us plug
. Then the maximum acceleration will be ![a_{max'}](https://tex.z-dn.net/?f=a_%7Bmax%27%7D)
![a_{max}=A\omega^2](https://tex.z-dn.net/?f=a_%7Bmax%7D%3DA%5Comega%5E2)
![a_{max'}=A(2\times \omega)^2\\a_{max'}=A\times 4\omega\\a_{max'}=4A\omega](https://tex.z-dn.net/?f=a_%7Bmax%27%7D%3DA%282%5Ctimes%20%5Comega%29%5E2%5C%5Ca_%7Bmax%27%7D%3DA%5Ctimes%204%5Comega%5C%5Ca_%7Bmax%27%7D%3D4A%5Comega)
![a_{max'}=4a_{max}](https://tex.z-dn.net/?f=a_%7Bmax%27%7D%3D4a_%7Bmax%7D)
We can see, when we double the angular velocity the maximum acceleration will changes by a factor of 4.
22. reduction
25. Le Chatelier's principle
The answer would be 27,000 Joules because (1/2) m v^2 =30*900 which equals 27,000 J
Answer:
0.54454
104.00902 N
Explanation:
m = Mass of wheel = 100 kg
r = Radius = 0.52 m
t = Time taken = 6 seconds
= Final angular velocity
= Initial angular velocity
= Angular acceleration
Mass of inertia is given by
![I=\dfrac{mr^2}{2}\\\Rightarrow I=\dfrac{100\times 0.52^2}{2}\\\Rightarrow I=13.52\ kgm^2](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7Bmr%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20I%3D%5Cdfrac%7B100%5Ctimes%200.52%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20I%3D13.52%5C%20kgm%5E2)
Angular acceleration is given by
![\alpha=\dfrac{\tau}{I}\\\Rightarrow \alpha=\dfrac{\mu fr}{I}\\\Rightarrow \alpha=\dfrac{\mu 50\times 0.52}{13.52}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B%5Ctau%7D%7BI%7D%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B%5Cmu%20fr%7D%7BI%7D%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B%5Cmu%2050%5Ctimes%200.52%7D%7B13.52%7D)
Equation of rotational motion
![\omega_f=\omega_i+\alpha t\\\Rightarrow \omega_f=\omega_i+\dfrac{\mu (-50)\times 0.52}{13.52}t\\\Rightarrow 0=60\times \dfrac{2\pi}{60}+\dfrac{\mu (-50)\times 0.52}{13.52}\times 6\\\Rightarrow 0=6.28318-11.53846\mu\\\Rightarrow \mu=\dfrac{6.28318}{11.53846}\\\Rightarrow \mu=0.54454](https://tex.z-dn.net/?f=%5Comega_f%3D%5Comega_i%2B%5Calpha%20t%5C%5C%5CRightarrow%20%5Comega_f%3D%5Comega_i%2B%5Cdfrac%7B%5Cmu%20%28-50%29%5Ctimes%200.52%7D%7B13.52%7Dt%5C%5C%5CRightarrow%200%3D60%5Ctimes%20%5Cdfrac%7B2%5Cpi%7D%7B60%7D%2B%5Cdfrac%7B%5Cmu%20%28-50%29%5Ctimes%200.52%7D%7B13.52%7D%5Ctimes%206%5C%5C%5CRightarrow%200%3D6.28318-11.53846%5Cmu%5C%5C%5CRightarrow%20%5Cmu%3D%5Cdfrac%7B6.28318%7D%7B11.53846%7D%5C%5C%5CRightarrow%20%5Cmu%3D0.54454)
The coefficient of friction is 0.54454
At r = 0.25 m
![\omega_f=\omega_i+\dfrac{0.54454 (-50)\times 0.52}{13.52}6\\\Rightarrow 0=60\times \dfrac{2\pi}{60}+\dfrac{0.54454 f\times 0.25}{13.52}6\\\Rightarrow 2\pi=0.06041f\\\Rightarrow f=\dfrac{2\pi}{0.06041}\\\Rightarrow f=104.00902\ N](https://tex.z-dn.net/?f=%5Comega_f%3D%5Comega_i%2B%5Cdfrac%7B0.54454%20%28-50%29%5Ctimes%200.52%7D%7B13.52%7D6%5C%5C%5CRightarrow%200%3D60%5Ctimes%20%5Cdfrac%7B2%5Cpi%7D%7B60%7D%2B%5Cdfrac%7B0.54454%20f%5Ctimes%200.25%7D%7B13.52%7D6%5C%5C%5CRightarrow%202%5Cpi%3D0.06041f%5C%5C%5CRightarrow%20f%3D%5Cdfrac%7B2%5Cpi%7D%7B0.06041%7D%5C%5C%5CRightarrow%20f%3D104.00902%5C%20N)
The force needed to stop the wheel is 104.00902 N