Question

# 5. [1pt] Consider a perfectly elastic collision between two objects of equal mass. Object 1 is...

5. [1pt]
Consider a perfectly elastic collision between two objects of equal mass. Object 1 is initially moving with a velocity v = 3.04 m/s while object 2 is at rest. What are the final velocities after the collision? Enter the final velocity of object 1 first.

6. [1pt]
If the objects have masses m1 = 1.69 kg and m2 = 4.04 kg, what are the final velocities of the objects after the collision if it is perfectly elastic? Enter the final velocity of object 1 first.

(5) For a perfectly elastic collision, when target object (object 2) is initially at rest, the final velocity of the two masses are given as -

v1' = [(m1 - m2) / (m1 + m2)]*v1

v2' = [2m1 / (m1 + m2)]*v1

In our case,

m1 = m2 = m

v1 = 3.04 m/s

plug-in these values in the above equation -

We find that -

v1' = 0

v2' = [2m / (m + m)]*3.04 = 3.04 m/s

Hence, final velocity of object 1 = 0

Final velocity of object 2 = 3.04 m/s (Answer)

(6) In this case, we have -

m1 = 1.69 kg, m2 = 4.04 kg

v1 = 3.04 m/s, v2 = 0

So, v1' = [(1.69 - 4.04) / (1.69 + 4.04)]*3.04

= [-2.35 / 5.73]*3.04 = -1.25 m/s

v2' = [2*1.69 / (1.69 + 4.04)]*3.04

= [2*1.69 / 5.73]*3.04 = 1.79 m/s

Hence,

final velocity of object 1 = -1.25 m/s (Negative sign shows that the direction of velocity is opposite to the initial velocity.]

Final velocity of object 2 = 1.79 m/s (Answer)

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