Physics, 31.03.2020 02:20 2019dawnmcmillan

6. A proton is released from rest 1.0 cm off a center of a uniformly charged disk of a 2.0 m radius carrying a +180 nC charge. What is the speed of the proton when it is 5 cm from the disk?

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Answer from: yadirachavez2002

the speed of the proton is v = 78.1 km/s

Explanation:

Generally Electric potential energy resulting from a proton can be mathematically represented as

$V(z) = \frac{Q(\sqrt{R^2 + z^2} - z )}{2 \pi \epsilon_o R^2}$

Where

R is the radius of the disc which is given as R = 2m

q is the charge on the proton with a value of $q = 1.602 *10^{-19}C$

the mass of this proton has a value of $m=1.673*10^{-27}kg$

z is the distance of the center of the disk from the question

$z_1 =1.0cm = \frac{1}{100} = 0.01m$

$z_2 = 5cm = \frac{5}{100} = 0.05m$

$\epsilon_0 = 8.85*10^{-12}F/m$

According the law of conservation of energy

The change in kinetic energy of the proton + change in electrostatic = 0

potential energy

The change in kinetic energy is $\Delta KE = \frac{1}{2} m (v^2 - u^2)$

Since u = 0 the equation becomes

$\Delta KE = \frac{1}{2} m (v^2)$

change in electrostatic potential energy is = q (V(z_1) - V(z_2))

Substituting this into the equation we have

$\frac{1}{2} mv^2 +q(V(z_1)- V(z_2)) = 0$

$\frac{1}{2} mv^2 = -q(V(z_1)- V(z_2))$

Recalling that $V(z) = \frac{Q(\sqrt{R^2 + z^2} - z )}{2 \pi \epsilon_o R^2}$ we have

$\frac{1}{2} mv^2 = -q(\frac{Q(\sqrt{R^2 +z_2^2}-z_2 )}{2 \pi \epsilon_0 R^2} - \frac{Q(\sqrt{R^2 +z_1^2}-z_1 )}{2 \pi \epsilon_0 R^2} )$

$\frac{1}{2} mv^2 = q(\frac{Q(\sqrt{R^2 +z_1^2}-z_1 )}{2 \pi \epsilon_0 R^2} - \frac{Q(\sqrt{R^2 +z_2^2}-z_2 )}{2 \pi \epsilon_0 R^2} )$

Substituting values $\frac{1}{2} mv^2 = 1.602*10^{-19}(\frac{180*10^{-9}(\sqrt{2^2 +0.01^2}-0.011 )}{2 \pi 8.85*10^{-12}* 2^2} - \frac{180*10^{-9}(\sqrt{2^2 +0.05^2}-0.05 )}{2 \pi *8.85*10^{-12} *2^2} )$

Making v the subject

$v=\sqrt{\frac{1.602*10^{-19}(\frac{180*10^{-9}(\sqrt{2^2 +0.01^2}-0.011 )}{2 \pi 8.85*10^{-12}* 2^2} - \frac{180*10^{-9}(\sqrt{2^2 +0.05^2}-0.05 )}{2 \pi *8.85*10^{-12} *2^2} )}{0.5 *1.673*10^{-27}}}$

v = 78.1 km/s

Answer from: Quest

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this. hope that you like the video and that it explains more in detail to you.

that is the link.

Answer from: Quest

answer;

d. are made mostly of liquid

explanation;

-the general composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.