Question

A small electrically charged aluminum sphere (mass 20.0 ?, charge −5.00 ??) is placed on a plastic tabletop. Your goal is to set up an electric field that will result in the sphere accelerating upwards at 13.0 ?⁄?^2 over a distance of 1.00 ?.

a) Draw a force diagram for the sphere while it is in motion.

b) Determine the magnitude and direction of the E-field required to make the sphere move in this particular way.

c) What assumptions did you make in part b.?

Answer 1

A)

======

B)

USING 2ND equation of motion

Net force acting on the particle = electric force in upward direction - gravitational force in downward direction

Now as per direction sense, we will take all upward forces as positive and all downward foeces as negative

So above equation becomes

m a = F - mg

F = m ( a + g)

Now Using conservation of energy

Gravitational potential energy = electric Potential energy

F h = q E d

[ 0.02* (9.8 + 13)] * 1 = 5* 10^-6* E * 1

E = 9.12* 10^4 N/C

========

C)

We assumed the following

* elecrtic field is uniform from its intial to final position i.e. 1 m above its final position

* no air resistance onthe path of particle during its upward acceleration

=====

Comment in case any doubt, will reply for sure.. Goodluck

mi Pecharge=546- DMC