Answer:
The ball stops instantaneously at the topmost point of the motion.
Explanation:
Assume we have thrown a ball up in the air. For that we have given a force on the ball and it acquires an initial velocity in the upward direction.
The forces that resist the motion of the ball in the upward direction are the force of gravity and air resistance. The ball will instantaneously come to rest when the velocity of the ball reduces to zero.
The two forces acting in the downward direction reduces its speed continuously and it becomes zero at the topmost point.
Answer:
a)N = 3.125 * 10¹¹
b) I(avg) = 2.5 × 10⁻⁵A
c)P(avg) = 1250W
d)P = 2.5 × 10⁷W
Explanation:
Given that,
pulse current is 0.50 A
duration of pulse Δt = 0.1 × 10⁻⁶s
a) The number of particles equal to the amount of charge in a single pulse divided by the charge of a single particles
N = Δq/e
charge is given by Δq = IΔt
so,
N = IΔt / e
![N = \frac{(0.5)(0.1 * 10^-^6)}{(1.6 * 10^-^1^9)} \\= 3.125 * 10^1^1](https://tex.z-dn.net/?f=N%20%3D%20%5Cfrac%7B%280.5%29%280.1%20%2A%2010%5E-%5E6%29%7D%7B%281.6%20%2A%2010%5E-%5E1%5E9%29%7D%20%5C%5C%3D%203.125%20%2A%2010%5E1%5E1)
N = 3.125 * 10¹¹
b) Q = nqt
where q is the charge of 1puse
n = number of pulse
the average current is given as I(avg) = Q/t
I(avg) = nq
I(avg) = nIΔt
= (500)(0.5)(0.1 × 10⁻⁶)
= 2.5 × 10⁻⁵A
C) If the electrons are accelerated to an energy of 50 MeV, the acceleration voltage must,
eV = K
V = K/e
the power is given by
P = IV
P(avg) = I(avg)K / e
![P(avg) = \frac{(2.5 * 10^-^5)(50 * 10^6 . 1.6 * 10^-^1^9)}{1.6 * 10^-^1^9}](https://tex.z-dn.net/?f=P%28avg%29%20%3D%20%5Cfrac%7B%282.5%20%2A%2010%5E-%5E5%29%2850%20%2A%2010%5E6%20.%201.6%20%2A%2010%5E-%5E1%5E9%29%7D%7B1.6%20%2A%2010%5E-%5E1%5E9%7D)
= 1250W
d) Final peak=
P= Ik/e
= ![= P(avg) = \frac{(0.5)(50 * 10^6 . 1.6 * 10^-^1^9)}{1.6 * 10^-^1^9}\\2.5 * 10^7W](https://tex.z-dn.net/?f=%3D%20P%28avg%29%20%3D%20%5Cfrac%7B%280.5%29%2850%20%2A%2010%5E6%20.%201.6%20%2A%2010%5E-%5E1%5E9%29%7D%7B1.6%20%2A%2010%5E-%5E1%5E9%7D%5C%5C2.5%20%2A%2010%5E7W)
P = 2.5 × 10⁷W
Answer:
![1.06085\times 10^{-10}\ m](https://tex.z-dn.net/?f=1.06085%5Ctimes%2010%5E%7B-10%7D%5C%20m)
Explanation:
h = Planck's constant = ![6.626\times 10^{-34}\ m^2kg/s](https://tex.z-dn.net/?f=6.626%5Ctimes%2010%5E%7B-34%7D%5C%20m%5E2kg%2Fs)
m = Mass of electron = ![9.11\times 10^{-31}\ kg](https://tex.z-dn.net/?f=9.11%5Ctimes%2010%5E%7B-31%7D%5C%20kg)
k = Coulomb constant = ![8.99\times 10^{9}\ Nm^2/C^2](https://tex.z-dn.net/?f=8.99%5Ctimes%2010%5E%7B9%7D%5C%20Nm%5E2%2FC%5E2)
e = Charge of electron = ![1.6\times 10^{-19}\ C](https://tex.z-dn.net/?f=1.6%5Ctimes%2010%5E%7B-19%7D%5C%20C)
n = 1 (ground state)
Angular momentum is given by
![L=mvr](https://tex.z-dn.net/?f=L%3Dmvr)
From Bohr's atomic model we have
![L=\dfrac{nh}{2\pi}](https://tex.z-dn.net/?f=L%3D%5Cdfrac%7Bnh%7D%7B2%5Cpi%7D)
![mvr=\dfrac{nh}{2\pi}\\\Rightarrow v=\dfrac{nh}{2\pi mr}](https://tex.z-dn.net/?f=mvr%3D%5Cdfrac%7Bnh%7D%7B2%5Cpi%7D%5C%5C%5CRightarrow%20v%3D%5Cdfrac%7Bnh%7D%7B2%5Cpi%20mr%7D)
The centripetal force will balance the electrostatic force
![\dfrac{ke^2}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow \dfrac{ke^2}{r}=mv^2\\\Rightarrow \dfrac{ke^2}{r}=m(\dfrac{nh}{2\pi mr})^2\\\Rightarrow r=\dfrac{n^2h^2}{4\pi^2mke^2}\\\Rightarrow r=\dfrac{1^2\times (6.626\times 10^{-34})^2}{4\pi^2 \times 9.11\times 10^{-31}\times 8.99\times 10^{9}\times (1.6\times 10^{-19})^2}\\\Rightarrow r=5.30426\times 10^{-11}\ m](https://tex.z-dn.net/?f=%5Cdfrac%7Bke%5E2%7D%7Br%5E2%7D%3D%5Cdfrac%7Bmv%5E2%7D%7Br%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bke%5E2%7D%7Br%7D%3Dmv%5E2%5C%5C%5CRightarrow%20%5Cdfrac%7Bke%5E2%7D%7Br%7D%3Dm%28%5Cdfrac%7Bnh%7D%7B2%5Cpi%20mr%7D%29%5E2%5C%5C%5CRightarrow%20r%3D%5Cdfrac%7Bn%5E2h%5E2%7D%7B4%5Cpi%5E2mke%5E2%7D%5C%5C%5CRightarrow%20r%3D%5Cdfrac%7B1%5E2%5Ctimes%20%286.626%5Ctimes%2010%5E%7B-34%7D%29%5E2%7D%7B4%5Cpi%5E2%20%5Ctimes%209.11%5Ctimes%2010%5E%7B-31%7D%5Ctimes%208.99%5Ctimes%2010%5E%7B9%7D%5Ctimes%20%281.6%5Ctimes%2010%5E%7B-19%7D%29%5E2%7D%5C%5C%5CRightarrow%20r%3D5.30426%5Ctimes%2010%5E%7B-11%7D%5C%20m)
The diameter is ![2\times 5.30426\times 10^{-11}=1.06085\times 10^{-10}\ m](https://tex.z-dn.net/?f=2%5Ctimes%205.30426%5Ctimes%2010%5E%7B-11%7D%3D1.06085%5Ctimes%2010%5E%7B-10%7D%5C%20m)
Answer:
Power is 1061.67W
Explanation:
Power=force×distance/time
Power=65×9.8×15/9 assuming gravity=9.8m/s²
Power=3185/3=1061.67W