Question

A ball of mass m hangs from a thread. A horizontal electric force F acts on the ball, such

that the thread makes an angle theta to the vertical.

(a) Find a general expression for the electric force F on the ball in terms of , m, and

the gravitational acceleration g. (please be descriptive with this question.

(b) Calculate F for = 34, m = 1:0 g, and g = 9:8m=s2.

(c) Calculate F for = 89:9, m = 1:0 g, and g = 9:8m=s2.

Sanity checks: Is answer to part c of the same order of magnitude as the force due to

gravity? Should it be? What about part d?

1

Answer 1

a) balancing forces for as shown in figure
F = Tsin(theta)
Fg = mg = Tcos(theta)
so,
dividing
F = mg*tan(theta)

b) F = (10^-3)*9.8*tan(34)= 6.61*10^-3 N

c) F = (10^-3)*9.8*tan(89.9)= 5.615 N

force due to gravity = mg = 9.8*10^-3 N

in part b) as angle is 34degree and tan34 = 0.6745
so,
answer to part b is of the same order of magnitude as the force due to gravity

whereas,
in part b) as angle is 89.9 degree and tan89.9 = 572.96
so,
answer to part c is not of the same order of magnitude as the force due to gravity