Kinetic Energy and Momentum in Air Track Puck Collision

In summary, the conversation discusses a diagram showing two pucks on a frictionless air track, where one has a mass of 8 kg and the other has a mass of 10.3 kg. Answering three questions about the pucks, it is determined that the lighter puck will cross the finish line first and have a larger kinetic energy due to its smaller mass. However, the conversation then delves into a discussion about momentum and how it may not necessarily be equal between the two pucks. It is then revealed that the bigger puck actually has a larger momentum, and this is explained through a formula involving kinetic energy and momentum. The conversation concludes with the speaker expressing gratitude for the help and discussing a previous experience with a similar question.
  • #1
twiztidmxcn
43
0
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
 

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  • #2
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 hav 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.
 
  • #3
thank you kindly friend

i figured my shiz naw out thanks to your help
 
  • #4
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

[tex]K = \frac{1}{2}\frac{p^2}{m} \rightarrow p = \sqrt{2Km}[/tex]

making the bigger puck the one with the biggest momentum.
 
  • #5
My mechanics teacher last semester fed us this question in an "oral quiz". We had like 30 seconds to find the answers :yuck:
 

1. How is impulse related to work?

Impulse is defined as the change in momentum of an object. In the context of work, impulse is the force applied over a certain period of time, which leads to a change in the object's velocity. This change in velocity is directly related to the work done on the object. The greater the impulse, the greater the change in velocity and the more work is done.

2. What is the formula for calculating work and impulse?

The formula for calculating work is W = F * d, where W is work, F is the force applied, and d is the displacement of the object. The formula for calculating impulse is J = F * Δt, where J is impulse, F is the average force applied, and Δt is the change in time over which the force is applied.

3. Can the work done on an object be negative?

Yes, the work done on an object can be negative. This occurs when the force applied and the displacement of the object are in opposite directions, resulting in a negative value for work. For example, if a person pushes a box up a ramp, the force applied is in the opposite direction of the displacement of the box, therefore resulting in negative work.

4. How does the angle between force and displacement affect work and impulse?

The angle between force and displacement affects both work and impulse. Work is maximized when the force and displacement are parallel to each other, and minimized when they are perpendicular. Similarly, impulse is maximized when the force and displacement are parallel, and minimized when they are perpendicular. This is because when the force and displacement are parallel, all of the force is directed towards the displacement, resulting in the greatest change in velocity and thus the greatest work and impulse.

5. Is there a relationship between work, impulse, and energy?

Yes, there is a relationship between work, impulse, and energy. Work is a measure of the energy transferred to an object, while impulse is a measure of the change in an object's momentum. Therefore, work and impulse are both forms of energy. Additionally, work and impulse both contribute to an object's kinetic energy, as they both involve the object's velocity and mass.

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