Kinetic Energy and Momentum in Air Track Puck Collision

[twiztidmxcn]

so i have a question about work and impulse:

The diagram shows an overhead view of two pucks on a frictionless air track. Puck 1 has a mass of 8 kg and puck 2 has a mass of 10.3 kg. The pucks begin at rest at the starting line. The pucks are pushed across the table by equal forces as a function of distance until they reach the finish line. Answer the following three questions about the pucks.

1) Which puck has larger kinetic energy?

A) 1, B) 2, C) same, D) unable to be determined

2) Which puck will cross the finish line first?

A) 1, B) 2, C) same, D) unable to be determined

3) Which puck has larger momentum?

A) 1, B) 2, C) same, D) unable to be determined

So, I know that the puck with smaller mass will cross the finish line first, which is puck 1, so the answer to question 2 is A.

My problem is, I've reasoned that should the same force be applied, the momentums would be equal, because although one has larger mass, the velocities will balance out, so equal momentums. The puck with larger kinetic energy would be the lighter puck for hte same reason.

This is not correct, and I can't really figure out why.

I know this is more of a conceptual question and harder to figure out with just straight math, so any help in the right direction would be much appreciated.

Thanks,
TwiztidMxcn

 

[whozum]

My problem is, I've reasoned that should the same force be applied, the momentums would be equal, because although one has larger mass, the velocities will balance out, so equal momentums. The puck with larger kinetic energy would be the lighter puck for hte same reason.

This is not correct, and I can't really figure out why.

Why would the velocities balance out? If one accelerates faster than the other, won't its velocity at different times be different? If one accelerated at 100m/s^2, will it have the same velocity crossing the finish line as the heavier one with 1m/s^2? This should help you with the momentum.

The energy, you know, is force times distance. They both travel the same distance, they both experience the same force.

 

[twiztidmxcn]

thank you kindly friend

i figured my shiz naw out thanks to your help

 

[quasar987]

A nice way to see 3) once you've figure out that the kinetic energies are the same is that the kinetic energy may be written

K = \frac{1}{2}\frac{p^2}{m} \rightarrow p = \sqrt{2Km}

making the bigger puck the one with the biggest momentum.

 

[quasar987]

My mechanics teacher last semester fed us this question in an "oral quiz". We had like 30 seconds to find the answers