(Note: Please be careful with roundoff error in this problem.) The drawing shows

Question

(Note: Please be careful with roundoff error in this problem.) The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 2 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 5.5 kg and is initially at rest. After the collision, the two pucks fly apart with the angles shown in the drawing. (a) Find the final speed of: puck A: m/s puck B: m/s (b) Find the kinetic energy of the A+B system: before the collision: J after the collision: J What type of collision is this?

Explanation / Answer

Using momentum conservation,

initial momentum = final momentum

2*5.5i + 5.5*0 = 2vA(cos65i + sin65j)   +   5.5vB(cos37i - sin37j)

11i +0j = (0.845vA+4.39vB)i + (1.81vA - 3.31vB)j

1.81vA - 3.31vB = 0

vA =1.83vB ..... (ii)

along i vector ( along the original line of motion)

0.845vA+4.39vB = 11

putting value of vA in terms of vB

1.54vB + 4.39vB = 11

vB = 1.85 m/s

vA = 1.83 x 1.85 =3.39 m/s

b) before collision = 2x5.5^2 /2 + 0 = 30.25 J

after collision = (2 x 3.39^2/2) + (5.5 x 1.85^2 /2) = 20.90 J

initial and final KE are not equal .

so it is Inelastic collision.

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