Answer:
![2.27\cdot 10^{49}](https://tex.z-dn.net/?f=2.27%5Ccdot%2010%5E%7B49%7D)
Explanation:
The gravitational force between the proton and the electron is given by
![F_G=G\frac{m_p m_e}{r^2}](https://tex.z-dn.net/?f=F_G%3DG%5Cfrac%7Bm_p%20m_e%7D%7Br%5E2%7D)
where
G is the gravitational constant
is the proton mass
is the electron mass
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,
![F_G=(6.67259\cdot 10^{-11} m^3 kg s^{-2})\frac{(1.67262\cdot 10^{-27}kg) (9.10939\cdot 10^{-31}kg)}{(3 m)^2}=1.13\cdot 10^{-68}N](https://tex.z-dn.net/?f=F_G%3D%286.67259%5Ccdot%2010%5E%7B-11%7D%20m%5E3%20kg%20s%5E%7B-2%7D%29%5Cfrac%7B%281.67262%5Ccdot%2010%5E%7B-27%7Dkg%29%20%289.10939%5Ccdot%2010%5E%7B-31%7Dkg%29%7D%7B%283%20m%29%5E2%7D%3D1.13%5Ccdot%2010%5E%7B-68%7DN)
The electrical force between the proton and the electron is given by
![F_E=k\frac{q_p q_e}{r^2}](https://tex.z-dn.net/?f=F_E%3Dk%5Cfrac%7Bq_p%20q_e%7D%7Br%5E2%7D)
where
k is the Coulomb constant
is the elementary charge (charge of the proton and of the electron)
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,
![F_E=(8.98755\cdot 10^9 Nm^2 C^{-2})\frac{(1.602\cdot 10^{-19}C)^2}{(3 m)^2}=2.56\cdot 10^{-19}N](https://tex.z-dn.net/?f=F_E%3D%288.98755%5Ccdot%2010%5E9%20Nm%5E2%20C%5E%7B-2%7D%29%5Cfrac%7B%281.602%5Ccdot%2010%5E%7B-19%7DC%29%5E2%7D%7B%283%20m%29%5E2%7D%3D2.56%5Ccdot%2010%5E%7B-19%7DN)
So, the ratio of the electrical force to the gravitational force is
![\frac{F_E}{F_G}=\frac{2.56\cdot 10^{-19} N}{1.13\cdot 10^{-68}N}=2.27\cdot 10^{49}](https://tex.z-dn.net/?f=%5Cfrac%7BF_E%7D%7BF_G%7D%3D%5Cfrac%7B2.56%5Ccdot%2010%5E%7B-19%7D%20N%7D%7B1.13%5Ccdot%2010%5E%7B-68%7DN%7D%3D2.27%5Ccdot%2010%5E%7B49%7D)
So, we see that the electrical force is much larger than the gravitational force.
Answer:
![\Delta V = 0.053 A](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%200.053%20A)
Explanation:
Electric field in a given region is given by equation
![E = \frac{A}{r^4}](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7BA%7D%7Br%5E4%7D)
as we know the relation between electric field and potential difference is given as
![\Delta V = -\int E. dr](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20-%5Cint%20E.%20dr)
so here we have
![\Delta V = - \int (\frac{A}{r^4}) .dr](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20-%20%5Cint%20%28%5Cfrac%7BA%7D%7Br%5E4%7D%29%20.dr)
![\Delta V = \frac{A}{3r_1^3} - \frac{A}{3r_2^3}](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20%5Cfrac%7BA%7D%7B3r_1%5E3%7D%20-%20%5Cfrac%7BA%7D%7B3r_2%5E3%7D)
here we know that
and ![r_2 = 2.89 m](https://tex.z-dn.net/?f=r_2%20%3D%202.89%20m)
so we will have
![\Delta V = \frac{A}{3}(\frac{1}{1.71^3} - \frac{1}{2.89^3})](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20%5Cfrac%7BA%7D%7B3%7D%28%5Cfrac%7B1%7D%7B1.71%5E3%7D%20-%20%5Cfrac%7B1%7D%7B2.89%5E3%7D%29)
so we will have
![\Delta V = 0.053 A](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%200.053%20A)
Answer:
0.25 m.
Explanation:
We'll begin by calculating the spring constant of the spring.
From the diagram, we shall used any of the weight with the corresponding extention to determine the spring constant. This is illustrated below:
Force (F) = 0.1 N
Extention (e) = 0.125 m
Spring constant (K) =?
F = Ke
0.1 = K x 0.125
Divide both side by 0.125
K = 0.1/0.125
K = 0.8 N/m
Therefore, the force constant, K of spring is 0.8 N/m
Now, we can obtain the number in gap 1 in the diagram above as follow:
Force (F) = 0.2 N
Spring constant (K) = 0.8 N/m
Extention (e) =..?
F = Ke
0.2 = 0.8 x e
Divide both side by 0.8
e = 0.2/0.8
e = 0.25 m
Therefore, the number that will complete gap 1is 0.25 m.
If a man pushes on a wall with some force then according to Newton's third law, wall will also apply force on man with same magnitude but opposite in direction.