A 4.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 2.

Question

A 4.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 2.9 kg object moving in the -x direction at 4.0 m/s. Find the final velocity of each mass for each of the following situations. (Take the positive direction to be +x.)
(a) The bodies stick together.
____m/s (4.5 kg mass)
____ m/s (2.9 kg mass)

(b) The collision is elastic.
____ m/s (4.5 kg mass)
_____m/s (2.9 kg mass)

(c) The 4.5 kg body is at rest after the collision.
____ m/s (4.5 kg mass)
___ m/s (2.9 kg mass)

(d) The 2.9 kg body is at rest after the collision.
____ m/s (4.5 kg mass)
______ m/s (2.9 kg mass)

(e) The 4.5 kg body has a velocity of 4.0 m/s in the -x direction after the collision.
____ m/s (4.5 kg mass)
___ m/s(2.9 kg mass)

Are the results in (c), (d), and (e) "reasonable"? Explain

Explanation / Answer

Remember: momentum = mass x velocity a) when the two masses stick together,they will have the same velocity (remember that they are moving in opposite directions) (4.5kg)(5.5m/s)-(2.9kg)(4.0m/s)=13.15 13.15/(4.5kg+2.9kg)=1.777 m/s b) if the collision is elastic, then each objects momentum is transferred to the other: (4.5kg)(5.5m/s)=24.75 24.75/2.9kg=8.534m/s for the 2.9 kg object (2.9kg)(4.0m/s)=11.6 11.6/4.5kg=2.578m/s for the 4.5 kg object c) In this scenario the 2.9kg block bounces back, keeping its momentum and adding the other: (4.5kg)(5.5m/s)+(2.9kg)(4.0m/s)=36.35 36.35/2.9kg=12.53m/s d) In this scenario the 4.5kg block bounces back, keeping its momentum and adding the other: (4.5kg)(5.5m/s)+(2.9kg)(4.0m/s)=36.35 36.35/4.5kg=8.078m/s e) set up a system of the before and after momentum: (4.5kg)(5.5m/s)+(2.9kg)(4.0m/s)=(4.5kg)(4.0m/s)+(2.9kg)(x) x=6.326m/s The numbers are reasonable, but the situations set up in (c), (d), and (e) are not reasonable. It is nearly impossible to ever get those scenarios to work out perfectly (without doing something else that would convert the momentum into something else like heat/friction).

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