Can someone explain how is this suppose to make sense(Physics)?!

[docbrill]

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So I was doing some Berkeley physics and apperantly this concept does not make any sense to me. On the first problem the question was what would happen with the distance between two rolling balls (down a hill) if one is released from rest and after some time the second ball is released from rest (hill and balls are the same). My intuition told me(which was apperantly wrong) that the distance would remain the same. However, the correct answer was that the first ball would always move faster, and therefore the distance would increase over time, go figure😕
Then, I had a problem with skiers sliding down a hill. The same conditions, and the same question. So, my intuition again told me that the distance would remain the same, since they had the same initial speed. However, I remembered that my intuition for the rolling case was wrong, so I went with what I have learned, i.e. the distance would increase because the first skier woul be moving faster. Of course, it was wrong, and it turned out that the distance would remain the same. Can someone please explain what the difference is between the two cases, and why is the distance increasing in the first case?

 

[txprodigal]

So I was doing some Berkeley physics and apperantly this concept does not make any sense to me. On the first problem the question was what would happen with the distance between two rolling balls (down a hill) if one is released from rest and after some time the second ball is released from rest (hill and balls are the same). My intuition told me(which was apperantly wrong) that the distance would remain the same. However, the correct answer was that the first ball would always move faster, and therefore the distance would increase over time, go figure😕
Then, I had a problem with skiers sliding down a hill. The same conditions, and the same question. So, my intuition again told me that the distance would remain the same, since they had the same initial speed. However, I remembered that my intuition for the rolling case was wrong, so I went with what I have learned, i.e. the distance would increase because the first skier woul be moving faster. Of course, it was wrong, and it turned out that the distance would remain the same. Can someone please explain what the difference is between the two cases, and why is the distance increasing in the first case?

The second situation you assumed they had the same initial speed, but the question doesn't say that. Thus, you need more information to determine the distance d.

In the first situation, the first ball is released prior the release of the second ball. If you look at the moment right when the second ball is released, you can think of the second ball as being released from rest while the first ball has an initial velocity. The first ball gains a velocity during the small period of time before the second ball is dropped, so it's velocity will always be greater than the second ball which results in the distance between the two balls increasing with time.

 

[docbrill]

txprodigal,
I actually didn't assume that their speeds were the same in the second case. I just gave this as hypothetical situation, since in the answer Berkeley stated that if the velocities were the same or zero, then the distance would remain the same. I thought about it and now it makes more sense when I relate it to the equation (which I did not know when I took the practice) Thanks for the response though, it makes sense.

 

[Nasem]

For first situation, think about if you were standing on a stationary helicopter 100 feet above the ground.

You have 2 rocks, both same size, shape, and mass... you "throw down" the first rock while only releasing the 2nd rock (both at the same time and same level...) What do you think is going to happen if you were an observer and your watching those 2 rocks fall down to the ground? You will notice that the first rock is always going to move further from the 2nd rock (because it was release with an initial velocity greater than zero)...

If you think about it, these rocks are in a "vacum" and I assume every speed / air resistance question in the MCAT is going to be vacum based... so technically speaking, objects fall to the ground with a = 9.8 m/s^2 and if this is a vacum, they will never reach a maximum velocity, so in our situation with the rocks, the first rock will always be traveling faster than rock #2 (there is no air resistance to having them reach a maximum velocity)

hope this helps

 

[WashMe]

velocity of a ball = initial velocity + acceleration*time

thus, at any instant the velocity of ball 1 = X (found by first a*t) + acceleration*time (where time=0 when ball 2 is dropped)

at any instant, the velocity of ball 2 = acceleration*time (where time=0 when ball 2 is dropped)

at any instant, (velocity of ball 1) - (velocity of ball 2) = X

Ball 1 will move away from ball 2 at a constant velocity equal to the velocity at which it was traveling when ball 2 hit the ground (denoted "X" above). The distance between the balls will increase linearly as a function of time.

cool?

I haven't taken physics in 2 years and I took the MCAT Jan. 2008, so someone please correct me if I'm wrong.