Answer:
Velocity of the electron at the centre of the ring, ![v=1.37\times10^7\ \rm m/s](https://tex.z-dn.net/?f=v%3D1.37%5Ctimes10%5E7%5C%20%5Crm%20m%2Fs)
Explanation:
<u>Given:</u>
- Linear charge density of the ring=
![0.1\ \rm \mu C/m](https://tex.z-dn.net/?f=0.1%5C%20%5Crm%20%5Cmu%20C%2Fm)
- Radius of the ring R=0.2 m
- Distance of point from the centre of the ring=x=0.2 m
Total charge of the ring
![Q=0.1\times2\pi R\\Q=0.1\times2\pi 0.4\\Q=0.251\ \rm \mu C](https://tex.z-dn.net/?f=Q%3D0.1%5Ctimes2%5Cpi%20R%5C%5CQ%3D0.1%5Ctimes2%5Cpi%200.4%5C%5CQ%3D0.251%5C%20%5Crm%20%5Cmu%20C)
Potential due the ring at a distance x from the centre of the rings is given by
![V=\dfrac{kQ}{\sqrt{(R^2+x^2)}}\\](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7BkQ%7D%7B%5Csqrt%7B%28R%5E2%2Bx%5E2%29%7D%7D%5C%5C)
The potential difference when the electron moves from x=0.2 m to the centre of the ring is given by
![\Delta V=\dfrac{kQ}{R}-\dfrac{kQ}{\sqrt{(R^2+x^2)}}\\\Delta V={9\times10^9\times0.251\times10^{-6}} \left( \dfrac{1}{0.4}-\dfrac{1}{\sqrt{(0.4^2+0.2^2)}} \right )\\\Delta V=5.12\times10^2\ \rm V](https://tex.z-dn.net/?f=%5CDelta%20V%3D%5Cdfrac%7BkQ%7D%7BR%7D-%5Cdfrac%7BkQ%7D%7B%5Csqrt%7B%28R%5E2%2Bx%5E2%29%7D%7D%5C%5C%5CDelta%20V%3D%7B9%5Ctimes10%5E9%5Ctimes0.251%5Ctimes10%5E%7B-6%7D%7D%20%5Cleft%28%20%5Cdfrac%7B1%7D%7B0.4%7D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B%280.4%5E2%2B0.2%5E2%29%7D%7D%20%5Cright%20%29%5C%5C%5CDelta%20V%3D5.12%5Ctimes10%5E2%5C%20%5Crm%20V)
Let
be the change in potential Energy given by
![\Delta U=e\times \Delta V\\\Delta U=1.67\times10^{-19}\times5.12\times10^{2}\\\Delta U=8.55\times10^{-17}\ \rm J](https://tex.z-dn.net/?f=%5CDelta%20U%3De%5Ctimes%20%5CDelta%20V%5C%5C%5CDelta%20U%3D1.67%5Ctimes10%5E%7B-19%7D%5Ctimes5.12%5Ctimes10%5E%7B2%7D%5C%5C%5CDelta%20U%3D8.55%5Ctimes10%5E%7B-17%7D%5C%20%5Crm%20J)
Change in Potential Energy of the electron will be equal to the change in kinetic Energy of the electron
![\Delta U=\dfrac{mv^2}{2}\\8.55\times10^{-17}=\dfrac{9.1\times10^{-31}v^2}{2}\\v=1.37\times10^7\ \rm m/s](https://tex.z-dn.net/?f=%5CDelta%20U%3D%5Cdfrac%7Bmv%5E2%7D%7B2%7D%5C%5C8.55%5Ctimes10%5E%7B-17%7D%3D%5Cdfrac%7B9.1%5Ctimes10%5E%7B-31%7Dv%5E2%7D%7B2%7D%5C%5Cv%3D1.37%5Ctimes10%5E7%5C%20%5Crm%20m%2Fs)
So the electron will be moving with ![v=1.37\times10^7\ \rm m/s](https://tex.z-dn.net/?f=v%3D1.37%5Ctimes10%5E7%5C%20%5Crm%20m%2Fs)
Answer:
V= 6.974 m/s
Explanation:
Component( box) weight acting parallel and down roof 88(sin39.0°)=55.4 N
Force of kinetic friction acting parallel and up roof = 18.0 N
Fnet force acting on tool box acting parallel and down roof
Fnet= 55.4 - 18.0
Fnet=37.4 N
acceleration of tool box down roof
a = 37.4(9.81)/88.0
a= 4.169 m/s²
d = 4.90 m
t = √2d/a
t= √2(4.90)/4.169
t= 1.662 s
V = at
V= 4.169(1.662)
V= 6.974 m/s
Answer:
0.07756 m
Explanation:
Given mass of object =0.20 kg
spring constant = 120 n/m
maximum speed = 1.9 m/sec
We have to find the amplitude of the motion
We know that maximum speed of the object when it is in harmonic motion is given by
where A is amplitude and
is angular velocity
Angular velocity is given by
where k is spring constant and m is mass
So ![v_{max}=A\sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=v_%7Bmax%7D%3DA%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
![A=V_{max}\sqrt{\frac{m}{k}}=1.9\times \sqrt{\frac{0.2}{120}}=0.07756 \ m](https://tex.z-dn.net/?f=A%3DV_%7Bmax%7D%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D%3D1.9%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.2%7D%7B120%7D%7D%3D0.07756%20%5C%20m)
Answer:
D. 2.5 Hz
Explanation:
Frequency = speed of wave / wavelength
= 335 /140 ( from graph)
= 2.4
The velocity with which the jumper leaves the floor is 5.1 m/s.
<h3>
What is the initial velocity of the jumper?</h3>
The initial velocity of the jumper or the velocity with which the jumper leaves the floor is calculated by applying the principle of conservation of energy as shown below.
Kinetic energy of the jumper at the floor = Potential energy of the jumper at the maximum height
¹/₂mv² = mgh
v² = 2gh
v = √2gh
where;
- v is the initial velocity of the jumper on the floor
- h is the maximum height reached by the jumper
- g is acceleration due to gravity
v = √(2 x 9.8 x 1.3)
v = 5.1 m/s
Learn more about initial velocity here: brainly.com/question/19365526
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