You have a lightweight spring whose unstretched length is 4.0 cm. First, you att

Question

You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 2.0 g mass from it. This stretches the spring to a length of 4.8 cm.You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.3 cm . Part A What is the magnitude of the charge (in nC) on each bead? Express your answer using two significant figures 50.12 nC Submit Previous Answers Request Answer

Explanation / Answer

The first part gives you the spring constant of the spring. When you put a force of 2.0 g times gravity (assuming you have a perfect massless spring - otherwise, the force on the spring would have to include its own weight plus the 2 g mass), you get 0.8 cm of displacement (4.8 cm - 4.0 cm). That tells you the spring constant:

F = - k x
(2 g) * (980 cm/s^2) = -k (0.8 cm)
k = -2450 g/s^s

Now you calculate the force on the spring with the charged beads on them:
F = -k x
= (2450g/s^2) * (4.3 cm - 4.0 cm)
= 735 dynes

So you know that the charge is enough to produce a force of 735 dynes at a separation of 4.3 cm.

F = (1/4*pi*e0) * q1*q2/r2
With q1 = q2, this rearranges to

q2 = 4*pi*e0*F * r2
=(4*pi*e0)* (735*10-5 N) * (0.043 m)2

=38.85nC or 39nC

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.