Question

An object with a mass of 7.00 g is moving to the right at 14.0 cm/s when it is overtaken by an object with a mass of 25.0 g moving in the same direction with a speed of 17.0 cm/s. If the collision is elastic, determine the speed of each object after the collision.

25.0-g object cm/s

7.00-g object cm/s

Answer 1

ELASTIC

m1 = 25 g                       m2 = 7 g

speeds before collision

u1 = 17 cm/s                          u2 = 14 cm/s

speeds after collision

v1 = ?                              v2 = ?

initial momentum before collision

Pi = m1*u1 + m2*u2

after collision final momentum

Pf = m1*v1 + m2*v2

from momentum conservation

total momentum is conserved

Pf = Pi

m1*u1 + m2*u2 = m1*v1 + m2*v2

m1*(u1-v1) = m2*(v2-u2) .....(1)

from energy conservation

total kinetic energy before collision = total kinetic energy after collision

KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2

KEf =   0.5*m1*v1^2 + 0.5*m2*v2^2

KEi = KEf

0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2

0.5*m1*(u1^2-v1^2) = 0.5*m2*(v2^2-u2^2).....(2)

solving 1&2

we get

u1 + v1 = v2 + u2

u1 - u2 = v2-v1

v2 = u1 - u2 + v1 ..........(3)

using 3 in 1

v1 = ((m1-m2)*u1 + (2*m2*u2))/(m1+m2)

v2 = ((m2-m1)*u2 + (2*m1*u1))/(m1+m2)

-----------------

v1(25 g) = ((25-7)*17 + (2*7*15))/(7+25)

v1 (25 g )= 16.125 cm/s

v2 (7 .00-g) = ((7-25)*14 + (2*25*17))/(7+25)

v2 (7 .00-g) = 18.7 cm/s