Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.300 kg and 0.700 kg, and uniformly distributed charges of -2.00 HC and 3.00 HC. 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 at r O greater o.) O the same O less than

Answer 1

For the lighter sphere: mı = 0.300 kg ri = 0.300 cm = 0.003 m For the heavier sphere: m2 = 0.700 kg r2 = 0.500 cm = 0.005 m Applying the conservation of linear momentum: Po = PF 0 = m1v1 – m2V2 m1v1 = m2V2 0.3v1 = 0.7v2 kq192 V1 = 502 Applying the conservation of energy: Eo = EF Ko + = KF +UF 0 kq192 1 ===mvi+m2vz +- lo 2 In this case: lo = 1.00 m I = 0.8 cm = 0.008 m Then: (9 x 10 (-2 x 10-6)(3 x 10-6) 1.00 .700v3 + (9 x 10(-2 x 10-6)(3 x 10-6) 0.008 Solving for vz V2 = 2.40 V1