Answer:
r2 = 1 m
therefore the electron that comes with velocity does not reach the origin, it stops when it reaches the position of the electron at x = 1m
Explanation:
For this exercise we must use conservation of energy
the electric potential energy is
U =
for the proton at x = -1 m
U₁ =
for the electron at x = 1 m
U₂ =
starting point.
Em₀ = K + U₁ + U₂
Em₀ =
final point
Em_f =
energy is conserved
Em₀ = Em_f
\frac{1}{2} m v^2 - k \frac{e^2}{r+1} + k \frac{e^2}{r-1} = k e^2 (- \frac{1}{r_2 +1} + \frac{1}{r_2 -1})
\frac{1}{2} m v^2 - k \frac{e^2}{r+1} + k \frac{e^2}{r-1} = k e²(
)
we substitute the values
½ 9.1 10⁻³¹ 450 + 9 10⁹ (1.6 10⁻¹⁹)² [
) = 9 109 (1.6 10-19) ²(
)
2.0475 10⁻²⁸ + 2.304 10⁻³⁷ (5.0125 10⁻³) = 4.608 10⁻³⁷ (
)
2.0475 10⁻²⁸ + 1.1549 10⁻³⁹ = 4.608 10⁻³⁷
r₂² -1 = (4.443 10⁸)⁻¹
r2 =
r2 = 1 m
therefore the electron that comes with velocity does not reach the origin, it stops when it reaches the position of the electron at x = 1m
Answer:
T
Explanation:
= Power of the bulb = 100 W
= distance from the bulb = 2.5 m
= Intensity of light at the location
Intensity of the light at the location is given as
![I = \frac{P}{4\pi r^{2}}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7BP%7D%7B4%5Cpi%20r%5E%7B2%7D%7D)
![I = \frac{100}{4(3.14) (2.5)^{2}}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B100%7D%7B4%283.14%29%20%282.5%29%5E%7B2%7D%7D)
= 1.28 W/m²
= maximum magnetic field
Intensity is given as
![I = \frac{B_{o}^{2}c}{2\mu _{o}}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7BB_%7Bo%7D%5E%7B2%7Dc%7D%7B2%5Cmu%20_%7Bo%7D%7D)
![1.28 = \frac{B_{o}^{2}(3\times 10^{8})}{2(12.56\times 10^{-7})}](https://tex.z-dn.net/?f=1.28%20%3D%20%5Cfrac%7BB_%7Bo%7D%5E%7B2%7D%283%5Ctimes%2010%5E%7B8%7D%29%7D%7B2%2812.56%5Ctimes%2010%5E%7B-7%7D%29%7D)
T
The velocity of tennis racket after collision is 14.96m/s
<u>Explanation:</u>
Given-
Mass, m = 0.311kg
u1 = 30.3m/s
m2 = 0.057kg
u2 = 19.2m/s
Since m2 is moving in opposite direction, u2 = -19.2m/s
Velocity of m1 after collision = ?
Let the velocity of m1 after collision be v
After collision the momentum is conserved.
Therefore,
m1u1 - m2u2 = m1v1 + m2v2
![v1 = (\frac{m1-m2}{m1+m2})u1 + (\frac{2m2}{m1+m2})u2](https://tex.z-dn.net/?f=v1%20%3D%20%28%5Cfrac%7Bm1-m2%7D%7Bm1%2Bm2%7D%29u1%20%2B%20%28%5Cfrac%7B2m2%7D%7Bm1%2Bm2%7D%29u2)
![v1 = (\frac{0.311-0.057}{0.311+0.057})30.3 + (\frac{2 X 0.057}{0.311 + 0.057}) X-19.2\\\\v1 = (\frac{0.254}{0.368} )30.3 + (\frac{0.114}{0.368}) X -19.2\\ \\v1 = 20.91 - 5.95\\\\v1 = 14.96](https://tex.z-dn.net/?f=v1%20%3D%20%28%5Cfrac%7B0.311-0.057%7D%7B0.311%2B0.057%7D%2930.3%20%2B%20%28%5Cfrac%7B2%20X%200.057%7D%7B0.311%20%2B%200.057%7D%29%20X-19.2%5C%5C%5C%5Cv1%20%3D%20%28%5Cfrac%7B0.254%7D%7B0.368%7D%20%2930.3%20%2B%20%28%5Cfrac%7B0.114%7D%7B0.368%7D%29%20X%20-19.2%5C%5C%20%5C%5Cv1%20%3D%2020.91%20-%205.95%5C%5C%5C%5Cv1%20%3D%2014.96)
Therefore, the velocity of tennis racket after collision is 14.96m/s