Question

In a region where there is a uniform electric field that is upward and has magnitude 3.60×10⁴ N/C ,a small object is projected upward with an initial speed of 2.32 m/s . The object travels upward a distance of 6.98 cm in 0.200 s.

What is the object's charge-to-mass ratio q/m (magnitude and sign)? Assume g = 9.80 m/s2, and ignore air resistance.

Answer 1

Using Force balance on particle

Fnet = Fe - Fg

m*a = q*E - m*g

m*(a + g) = q*E

q/m = (a + g)/E

Using given values:

E = 3.6*10^4 N/C

g = 9.80 m/sec^2

Using kinematic equation

d = u*t + 0.5*a*t^2

d = 6.98 cm = 0.0698 m

0.0698 = 2.32*0.200 + 0.5*a*0.200^2

a = 2*(0.0698 - 2.32*0.200)/0.200^2

a = -19.71 m/sec^2

So,

q/m = (-19.71 + 9.80)/(3.60*10^4)

|q/m| = -2.75*10^-4 C/kg

Since object is moving upward in an electric field that is also upward, So Charge should be negative

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