OK.....the y velocity is .0135/t where t is the time it took to travel 56 cm at (4 x 103m/s) = .56/412
.0135/ (.56/412) = ( .0135 x 412) /.56 = 9.932 m/s
This velocity change from ZERO to this value occured in the time it took to cover the plate length of 26cm (.26m) at 4 x 103 m/s.
(is this written properly? 4 x 103 m/s?) 412m/s (pretty slow) .26/412 = .00063107 seconds
Acceleration in the y direction is thus the change in
velocity/time = (9.932)/.00063107 = 15738.4 m/s^2
Since F= ma Thus the force is 15738.4 ( m )
Lorentz force law : F= q(E+ v x B) = 15738.4 m divide both sides by m
q/m (E + v x B) = 15738.4
q/m = 15738.4/ (E + v x B) We are given E and v which we can substitute....but we still do not have 'B' the magnetic flux density......hmmmmm .... NOW I'M STUCK! Wonder if I was given all of the information? And was the initial speed really 4 x 103 m/s ?
Think I might be on the wrong path???
I'll get back to this shortly, but I think the key is to recognize the 'x' velocity does not change.....the acceleration of the particle is the velocity imparted in the 'y' direction and it is 1.35/56 proportional to the initial 'x' velocity of 4 x 103 m/s then you can use : (Lorentz force law) and Newtons second law to calculate B then m/q a = E + v x B More later.....gotta run....
Let's get the top and bottom surface areas first
t=pi r^2 = pi (18^2) = 1017.876
b=pi r^2 = pi (36^2) =4071.504 (IF we are counting the bottom)
the 'Middle surface area is just the difference betwen these two 4071.504 - 1017.876 = 3053.628
Now the sides are pi x d x h
Bottom pi x 72 x 18 =4071.504
top pi x 36 x 18 = 2035.752
Now add them all together:
2035.752 + 4071.504 + 3053.628 + 4071.504 + 1017.876 = USE calculator
NOTE: IF BOTTOM is not cosidered part of the 'Surface Area' leave out ONE of the 4071.504 terms.
(14250.264 sq in)