Answer:
t = 2.58*10^-6 s
Explanation:
For a nonconducting sphere you have that the value of the electric field, depends of the region:
![rR:\\\\E=k\frac{Q}{r^2}](https://tex.z-dn.net/?f=r%3CR%3A%5C%5C%5C%5CE%3Dk%5Cfrac%7BQr%7D%7BR%5E3%7D%5C%5C%5C%5Cr%3ER%3A%5C%5C%5C%5CE%3Dk%5Cfrac%7BQ%7D%7Br%5E2%7D)
k: Coulomb's constant = 8.98*10^9 Nm^2/C^2
R: radius of the sphere = 10.0/2 = 5.0cm=0.005m
In this case you can assume that the proton is in the region for r > R. Furthermore you use the secon Newton law in order to find the acceleration of the proton produced by the force:
![F=m_pa\\\\qE=m_pa\\\\k\frac{qQ}{r^2}=m_pa\\\\a=k\frac{qQ}{m_pr^2}](https://tex.z-dn.net/?f=F%3Dm_pa%5C%5C%5C%5CqE%3Dm_pa%5C%5C%5C%5Ck%5Cfrac%7BqQ%7D%7Br%5E2%7D%3Dm_pa%5C%5C%5C%5Ca%3Dk%5Cfrac%7BqQ%7D%7Bm_pr%5E2%7D)
Due to the proton is just outside the surface you can use r=R and calculate the acceleration. Also, you take into account the charge density of the sphere in order to compute the total charge:
![Q=\rho V=(5.5*10^{-6}C/m^3)(\frac{4}{3}\pi(0.05m)^3)=2.87*10^{-9}C\\\\a=(8.98*10^9Nm^2/C^2)\frac{(1.6*10^{-19}C)(2.87*10^{-9}C)}{(1.67*10^{-27}kg)(0.05m)^2}=9.87*10^{11}\frac{m}{s^2}](https://tex.z-dn.net/?f=Q%3D%5Crho%20V%3D%285.5%2A10%5E%7B-6%7DC%2Fm%5E3%29%28%5Cfrac%7B4%7D%7B3%7D%5Cpi%280.05m%29%5E3%29%3D2.87%2A10%5E%7B-9%7DC%5C%5C%5C%5Ca%3D%288.98%2A10%5E9Nm%5E2%2FC%5E2%29%5Cfrac%7B%281.6%2A10%5E%7B-19%7DC%29%282.87%2A10%5E%7B-9%7DC%29%7D%7B%281.67%2A10%5E%7B-27%7Dkg%29%280.05m%29%5E2%7D%3D9.87%2A10%5E%7B11%7D%5Cfrac%7Bm%7D%7Bs%5E2%7D)
with this values of a you can use the following formula:
![a=\frac{v-v_o}{t}\\\\t=\frac{v-v_o}{a}=\frac{2550*10^3m/s-0m/s}{9.87*10^{11}m/s^2}=2.58*10^{-6}s](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv-v_o%7D%7Bt%7D%5C%5C%5C%5Ct%3D%5Cfrac%7Bv-v_o%7D%7Ba%7D%3D%5Cfrac%7B2550%2A10%5E3m%2Fs-0m%2Fs%7D%7B9.87%2A10%5E%7B11%7Dm%2Fs%5E2%7D%3D2.58%2A10%5E%7B-6%7Ds)
hence, the time that the proton takes to reach a speed of 2550km is 2.58*10^-6 s
Answer:
The car would travel after applying brakes is, d = 14.53 m
Explanation:
Given that,
The time taken to apply brakes fully is, t = 0.5 s
The velocity of the car, v = 29.06 m/s
The distance traveled by the car in 0.5 s, d = ?
The relation between the velocity, displacement, and time is given by the formula
d = v x t m
Substituting the values in the above equation,
d = 29.06 m/s x 0.5 s
= 14.53 m
Therefore, the car would travel after applying brakes is, d = 14.53 m
Answer:
The minimum wall thickness required for the spherical tank is 0.0189 m
Explanation:
Given data:
d = inside diameter = 8.1 m
P = internal pressure = 1.26 MPa
σ = 270 MPa
factor of safety = 2
Question: Determine the minimum wall thickness required for the spherical tank, tmin = ?
The allow factor of safety:
![\sigma _{a} =\frac{\sigma }{factor-of-safety} =\frac{270}{2} =135MPa](https://tex.z-dn.net/?f=%5Csigma%20_%7Ba%7D%20%20%3D%5Cfrac%7B%5Csigma%20%7D%7Bfactor-of-safety%7D%20%3D%5Cfrac%7B270%7D%7B2%7D%20%3D135MPa)
The minimun wall thickness:
![t=\frac{Pd}{4\sigma _{a} } =\frac{1.26*8.1}{4*135} =0.0189m](https://tex.z-dn.net/?f=t%3D%5Cfrac%7BPd%7D%7B4%5Csigma%20_%7Ba%7D%20%7D%20%3D%5Cfrac%7B1.26%2A8.1%7D%7B4%2A135%7D%20%3D0.0189m)
The one at the base would be much older due to the law of super position, and the rock at the top would be much newer,again, due to the law of super position.
<span>The inner planets (in order of distance from the sun, closest to furthest) are Mercury, Venus, Earth and Mars. After an asteroid belt comes the outer planets, Jupiter, Saturn, Uranus and Neptune. The interesting thing is, in some other planetary systems discovered, the gas giants are actually quite close to the sun</span>