Two parallel plates are a distance apart with a potential difference between them. a point charge moves from the negatively char
1 answer:
Answer:
We can relate the kinetic energy of the particle to the potential difference between the plates by following equations:
Work energy theorem:
So,
If the distance is doubled and the potential difference is halved, then
Explanation:
As can be seen from the relationship between kinetic energy and the potential difference, the distance between the plates has no effect on the relation between kinetic energy and the potential difference. Since the charge of the second particle is equal to that of the first one, the new kinetic energy would be half of the first kinetic energy.
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1.
For the first part, we just need to write the equation of the forces along two perpendicular directions.
We have actually only two forces acting on the car, if we want it to go around the track without friction:
- The weight of the car, mg, downward
- The normal reaction of the track on the car, N, which is perpendicular to the track itself (see free-body diagram attached)
By resolving the normal reaction along the horizontal and vertical direction, we find the following equations:
(1)
(2)
where in the second equation, the term represents the centripetal force, with v being the speed of the car and R the radius of the track.
Dividing eq.(2) by eq.(1), we get the following expression:
2.
In this second situation, the cars moves around the track at a speed
This means that the centripetal force term
is now larger than before, and therefore, the horizontal component of the normal reaction, , is no longer enough to keep the car in circular motion.
This means, therefore, that an additional radial force F is required to keep the car round the track in circular motion, and therefore the equation becomes
And re-arranging for F,
(3)
But from eq.(2) in the previous part we know that
So, susbtituting into eq.(3),