Momentum (Your intuition)

[ilovemcat]

If you have EK 1001 Physics, glance at #400 to 409:

Do you think you could answer these questions on intuition alone? It seems fairly complex. Many of these questions could be answered using the graph EK provides, but I'm not sure if it's worth memorizing. What do you think?

Here's two sample questions for those that don't have the book:

A small object moving at 10 m/s to the right collides with a heavier object that is initially stationary. Which of the following is NOT a possible velocity of the smaller object after the collision?

A. 1 m/s to the right
B. 5 m/s to the right
C. 1 m/s to the left
D. 5 m/s to the left

(This question refers to a diagram where a Bob is swung from a height h and allowed to collide with a second bob (m2) at rest. Both bobs are the same size):

As the mass of m1 becomes much greater than m2, what is the maximum velocity that can be reached by m1 after the collision? (Note: Assume a completely elastic collision.)

A. 0 m/s
B. v
C. 2v
D. The maximum velocity is infinite















The answers to these questions is: B for question 1 and 2

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[Rabolisk]

I used intuition backed by a bit of mathematical reasoning, though not complex calculations. For the first one, the one that immediately stood out to me was B. First, a light object can easily bounce off of a heavy object in the opposite direction, so C and D were ruled out. When a light object hits a heavy object, it can stick to the heavy object and both can move to the right. If the light object has a mass of m with a velocity of v, and the heavy object's mass is > m, then the total mass is > 2m when the objects stick together. Conservation of momentum tells you that velocity has to be < 1/2v, so 5 m/s is not possible. If I saw this question on the MCAT, I would immediately look to B based on intuition, but I would do this math to confirm my suspicion.

For the second question, we have not only conservation of momentum but also that of kinetic energy. We have m1v1i (before collision) = m1v1f + m2v2f. But if m1 >>> m2, then m2v2f is trivial compared to m1v1f. If m1v1i = m1v1f (m2v2f negligible), then both momentum and kinetic energy are conserved. You get that v1f = v1i. This question is tough, but doable.

 

[ilovemcat]

I used intuition backed by a bit of mathematical reasoning, though not complex calculations. For the first one, the one that immediately stood out to me was B. First, a light object can easily bounce off of a heavy object in the opposite direction, so C and D were ruled out. When a light object hits a heavy object, it can stick to the heavy object and both can move to the right. If the light object has a mass of m with a velocity of v, and the heavy object's mass is > m, then the total mass is > 2m when the objects stick together. Conservation of momentum tells you that velocity has to be < 1/2v, so 5 m/s is not possible. If I saw this question on the MCAT, I would immediately look to B based on intuition, but I would do this math to confirm my suspicion.

For the second question, we have not only conservation of momentum but also that of kinetic energy. We have m1v1i (before collision) = m1v1f + m2v2f. But if m1 >>> m2, then m2v2f is trivial compared to m1v1f. If m1v1i = m1v1f (m2v2f negligible), then both momentum and kinetic energy are conserved. You get that v1f = v1i. This question is tough, but doable.

That's intense, haha. I'm praying something like this won't show up. I can't stuff another graph into my memory.