Question

A 27.5-g object moving to the right at 19.0 cm/s overtakes and collides elastically with a 11.5-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)
27.5-g object cm/s?

11.5-g object cm/s?

Answer 1

Answer:

After collision, velocity of massive object 27.5 g has reduced from 19 cm/s to 16.64 cm/s while that of lighter object 11.5 has increased from 15 cm/s to 20.64 cm/s because of elastic collision.

Explanation:

As, this question has two parts: a) We have to find the velocity after the collision with the mass of the object 27.5 g.

b) We have to find the velocity with 11.5 g mass of the object.

Now,

In this case the massive body collides with the lighter body. As we know;

Mass of massive object = m1 = 27.5 g

Velocity of m1 before collision = v1 = 19 cm/s

mass of lighter object = m2 = 11.5 g

velocity of m2 before collision = v2 = 15 cm/s

We have to find the velocity of m1 and m2 after the collision

a)

Velocity of 27.5 g object after collision = v1' = ?

v1' = (m1-m2)/(m1+m2)×v1 + 2×m2/(m1+m2)×v2

v1' = (27.5-11.5)/27.5+11.5)×(19) + 2×(11.5)/(27.5+11.5)×(15)

v1' = 7.795 + 8.846

v1' = 16.64 cm/s.

b)

Velocity of 11.5 g object after collision = v2' = ?

v2' = 2×m1/(m1+m2)×v1 + (m2-m1)/(m1+m2)×v2

v2' = 2×(27.5)/(27.5+11.5)×(19) + (11.5-27.5)/(27.5+11.5)×(15)

v2' = 26.795 + (-6.154)

v2' = 20.641 cm/s.