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.
