NOTE: The numbers in this problem are NEW! Similar to Chapter 18 #44: An ideal s

Question

NOTE: The numbers in this problem are NEW! Similar to Chapter 18 #44: An ideal spring with an unstrained length of L 0.055 m and a spring constant of k-2.6 N/m hangs vertically downward from, the ceiling. A uniform electric ield fills the region containing the spring. A sphere with a mass of m= 7.8 10 kg anda net charge of ,--8.7 ?C is attached to the lower end of the spring. The sphere is released slowly, until it reaches equilibrium. The equilibrium length of the spring, with the sphere attached, is Lj= 0.075 m. Draw a free body diagram showing the forces acting on the sphere. What is the magnitude of the external electric field, E What is the direction of the external electric field (up or down)? a) b) c) Spring with mass/ charge attached in electric field Unstrained spring L1 (Similar to Ch. 18, Problem #44 FROM: PHYSICS, 10h Edition, Cutnell and Johnson, John Wiley & Sons, page 511

Explanation / Answer

a)The Hooks force acts up, gravity acts down and electric field balances this net force. By pulling it up.

b)The elongation is:

x = Lf - Li = 0.075 - 0.055 = 0.02 m

The net force will be:

q E = mg - kx

E = (mg - kx)/q

E = (0.0078 x 9.81 - 2.6 x 0.02)/(8.7 x 10^-6) = 2.82 x 10^3 N/C

Hence, E = 2.82 x 10^3 N

c)Upwards

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