A particle with mass 4.00 g and charge +10.0 A particle with mass 4.00 g and cha

Question

A particle with mass 4.00 g and charge +10.0

A particle with mass 4.00 g and charge +10.0 mu C enters through a small hole in a metal plate with a speed of 10.00 m/s at an angle of 55 degree . The uniform field in the region above the plate has magnitude 7.00 103 N/C and is directed downward. The region above the metal plate is essentially a vacuum, so there is no air resistance. Can you neglect the force of gravity when solving for the horizontal distance traveled by the particle? yes or no. Why or why not? How far will the particle travel, ?x, before it hits the metal plate? m

Explanation / Answer

acceleraion due to the electric field = charge of particle * electic field / mass of partical

so.. acceleratin = 10 * 10^(-6) * 7 * 10^3 / ( 4 * 10^-3 ) = 17.5 m/sec2

now accelriaon due to gravity = 9.8 m/sec2

a)

as acceletaion due to gravity is comparable

so. we cannot neglect for of gravity .

b) now, this can be taken as a projectile .. with total downward acceleraion = 17.5 + 9.8 = 27.3 m/sec2

for the particle ..

along y direction

intial velocity = uy = 10*sin 55 = 8.19152 m/sec

acceletaion = ay = -27.3 m/sec2 ( -ve as it is downward )

let the time taken be t..

for hitting the plate back, the total distance travelled = 0

so.. sy = 0

so.. sy = uy * t + 0.5 * ay * t^2

0 = 8.19152 * t - 0.5 * 27.3 * t^2

so.. t = 0.6001114 secs

along x - direction..

velocity = ux = 10*cos 55 = 5.7358 m/sec

so.. delta x = 5.7358 * 0.6001114 = 3.44212 m

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