Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.200 kg and 0.7

Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.200 kg and 0.700 kg, and uniformly distributed charges of -2.00 uC and 3.00 uC. They are released from rest when their centers are separated by 1.00 m (a) How fast will each be moving when they collide? (Hint: Consider conservation of energy and of linear momentum.) m/s (lighter sphere) m/s (heavier sphere) (b) If the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? (Note: Assume a reference level of potential V 0 atr) less than the same greater Explain your answer

Explanation / Answer

a)

When two charged spheres are at a distance ‘d’ from each other their electric PE is

Ui = kq1q2/di -------------(1)

When these spheres collides d=0m

Uf = kq1q2/df = 0 -------------(2)

U = kq1q2/di -------------(3)

U = - KE

kq1q2/di = ½* m1v1f2+ m2v2f2 -------------------(4)

Let us law of conservation of linear momentum when they collide,

m1v1i+ m2v2i= m1v1f+ m2v2f

since v1i= v1i= 0 m/s

m1v1f+ m2v2f =0

m1v1f = -m2v2f

v2f = -v1f *(m1/m2) = -2/7*v1f ---------------(5)

Put 5) in (4)

kq1q2/di = ½* m1v1f2+ m2*(2/7*v1f)2

Plugging values,

(9*10^9*2*10^-6*3*10^-6)/1^2 = ½*0.2*v1i2+ 0.7*(2/7*v1f)2

v1f = 0.65m/s ……………lighter sphere

v2f = -2/7*v1f = -2/7*0.59 = - 0.18m/s …………….heavier sphere

b)

Speeds for conductors will be same,

Because speed depends on values of charges and distance between two sphere only.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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