Work and Kinetic Energy and elastic collision

[siemieniuk]

hey all... have a question:

a body of 2 kg mass makes an elastic collision with another body at rest and afterwards continues to move in the original direction but with one-fourth of it's original speed. What is the mass of the struck body?

I started with comparing kinetic energy, then took a look at momentum... but I'm just not sure how I can solve for body #2's mass when I don't have a resultant velocity or anything... please point me in the right direction.

Thanks

 

[FZ+]

But you do have a resultant velocity, as it is elastic. Therefore, speed of approach must equal the relative speed after the collision.

V = Z - W

Where V is the initial velocity, Z is the resulting velocity of the struck object, and W is the resulting velocity of the first object.

 

[Banana]

Let V be final velocity and v be initial velocity of the 2 kg mass. Take the basic equation and multiply each side by v:

V/v = [(m1-m2)/(m1 + m2)]

We know that the ratio of V/v = 1/4. Therefore

1/4 = (m1 - m2)/(m1 + m2)

Cross multiply:

m1 + m2 = 4m1 - 4m2

0 = 3m1 - 5m2

0 = 3 (2 kg) - 5 m2

 

[Banana]

Sorry; I meant divide each side by v

 

[siemieniuk]

thanks... appreciate it more than you know