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Old Apr 5th 2013, 03:00 PM   #1
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Distance ?

Good morning/evening <3

For my problem,

A metal ball with a mass of 3x10^-6 kg and a charge of +5 mC has a kinetic energy of 6x10^8 j. it's directly at an infinite plane of charge with a charge distribution of +4c/m^2. if it's currently 1m away from the plane of charge, how close will it come to the plane before stopping?


(the correct answer is: 0.266 m)


-----------------------------------------------------------

(my attemp):

1- finding v2 from Ek = ½mv2
I get v= 20x10^6 m/s

2- F=ma
qE=ma
a= qE/m

3- find E by :

= 2.26x10^11

4- a=3.77x10^14 m/s^s

5- finally:

vf2 = vi2 + 2ad

d= vi2 /2a = 0.530 m

so, 1-0.530 = 0.47m


could any one tell me what's wrong?
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Old Apr 5th 2013, 04:08 PM   #2
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Given the data you provided, I believe your answer is correct. A way to do this that offers a slight shortcut is this:

Work = change in KE, and work = Force x distance, so distance = change in KE/force.

Change in KE is 6E+8 Joules
Force = Eq = 1.13E+9 N

So d= 6E+8 Joules/1.13E+9 N = 0.531 m. And as you say, 1 - 0.531m = 0.469m
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Old Apr 5th 2013, 04:18 PM   #3
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Originally Posted by Saloom View Post
Good morning/evening <3

For my problem,

A metal ball with a mass of 3x10^-6 kg and a charge of +5 mC has a kinetic energy of 6x10^8 j. it's directly at an infinite plane of charge with a charge distribution of +4c/m^2. if it's currently 1m away from the plane of charge, how close will it come to the plane before stopping?


(the correct answer is: 0.266 m)


-----------------------------------------------------------

(my attemp):

1- finding v2 from Ek = ½mv2
I get v= 20x10^6 m/s

2- F=ma
qE=ma
a= qE/m

3- find E by :

= 2.26x10^11.....UNITS? Is it V/m ?

4- a=3.77x10^14 m/s^s

5- finally:

vf2 = vi2 + 2ad

d= vi2 /2a = 0.530 m

so, 1-0.530 = 0.47m


could any one tell me what's wrong?
The current kinetic energy (when 1 m from the plate) is 6×10^8 J. I don't think you have to find the velocity .. just use Conservation of Energy.

The change of Kinetic Energy is -6×10^8 J when the velocity has fallen to zero.
The change of electric potential is deltaV = E*d (Volts)
so multiply by Q to get the change of potential energy (V*C = J);
Q*E*d = 6×10^8 J
The only unknown is d.

I get d=0.531 m .. same as you .. final position 0.469 m from plate

Have you checked that all the numbers are as given? Why do you believe the correct answer is 0.266 m?
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