Question

Bookmark An object with a mass of 5.00 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 18.0 cm/s. If the collision is elastic, determine the speed of each object after the collision.

25.0-g object ____ cm/s

5.00-g object ____cm/s

Answer 1

m1 = 5 gm   u1 = 14 cm/s v1=?

m2 = 25gm u2 =18 cm/s v2=?

using conservation of momentum we get,

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

5* 14 + 25* 18 = 5*v1 + 25*v2

520 = 5*v1 + 25*v2

104 - 5v2 = v1      ---------------------------(1)

using conservation of energy we get,

1/2*m1*(u1)² + 1/2*m2*(u2)² = 1/2*m1*(v1)² + 1/2*m2*(v2)²

5590 = 2.5*(v1)² +12.5*(v2)² --------------------------(2)

now substituting value of v1 from equation 1 in equation 2

we get,

5590 = 2.5*(104 - 5v2 )² +12.5*(v2)²

2236 = (104 - 5v2 )² + 5*(v2)²

solving the above quadratic equation we get,

so v2= 13.53 cm/sec

hence v1 = 36.35 cm/sec