Question

A ball of mass 1.0 kg and a ball of mass 3.0 kg are initially separated by 4.0 m in a region of space in which they interact only with one another. When the balls are released from rest, they accelerate toward one another. When they are separated by 2.0 m, how fast is each ball going?

Answer 1

let m1 = 1 kg, m2 = 3 kg

d1 = 4 m, d2 = 2 m

let v1 and v2 are the speeds of m1 and m2 when they come close to each other.

Apply conservation of momentum

m1*v1 = m2*v2

v1 = (m2/m1)*v2

(3/1)*v2

v1 = 3*v2 ----(1)

Apply conservation of energy

Ui + KEi = Uf + KEf

-G*m1*m2/d1 + 0 = -G*m1*m2/d2 + (1/2)*m1*v1^2 + (1/2)*m2*v2^2

G*m1*m2*(1/d2 - 1/d1) = (1/2)*m1*(3*v2)^2 + (1/2)*m2*v2^2

6.67*10^-11*1*3*(1/2 - 1/4) = (1/2)*1*(3*v2)^2 + (1/2)*3*v2^2

==> v2 = 2.89*10^-6 m/s <<<<<<<<<<------------------Answer

v1 = 3*v2

= 3*2.89*10^-6

= 8.67*10^-6 m/s <<<<<<<<<<------------------Answer