2 physics questions

[rinsterman12]

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First question is, tom, who has a mass of 80kg, and mary, who has a mass of 50kg, jump off a 20 tall building and land on a fire net. The net compresses, and they bounce back up at the same time.
One of the answer choices states that toms change of momentum is 3200 kg m/s. I found the velocity to be 20 m/s from his kinetic energy; one thing that I am confused about is this--- 80kg (v sub i -(-velocity sub i) = 3200. I thought change in momentum would be 80kg x final velocity, which should be -20 - 80kg x initial velocity, which should be 0? Please help I obviously am flawed somewhere in my logic.

The second question comes from a box sliding up a ramp at a 30 degree angle attached to a pully system. What is the acceleration of a 20 kg box if a force of 100 newtons is applied? Supposedly the 100 newtons is amplified by 2 thus making 200 newtons pulling on the box in the upward direction. I thought the force acting on the pulley system would in fact distribute evenly and come to 50 newtons. This is the only part of the question I do not understand. Please help and thank you.

 

[RogueUnicorn]

question 1: remember momentum, like velocity, is a vector.

question 2: i'm not really getting a mental picture of what's going on here, where is the force being applied and what else is attached to the pulley

 

[rinsterman12]

The diagram in the book is a box sitting on an incline. A rope is attached to the right side of the box. The rope extends to a two pulley system. Then the diagram has an arrow pointing downward denoting the force 100 newton force on the box. I hope that explains it. If not could someone tell me how to post a picture.
The first question, I understand that momentum has a vector put still don't understand how they represented their equation such that mass x (velocity initial - -velocity initial; I thought it was mass ( velocity final - velocity initial). Is the final velocity 0 or does it stay 20 m/s; I don't understand

 

[Bleg]

First question is, tom, who has a mass of 80kg, and mary, who has a mass of 50kg, jump off a 20 meter tall building and land on a fire net. The net compresses, and they bounce back up at the same time.
One of the answer choices states that toms change of momentum is 3200 kg m/s. I found the velocity to be 20 m/s from his kinetic energy; one thing that I am confused about is this--- 80kg (v sub i -(-velocity sub i) = 3200. I thought change in momentum would be 80kg x final velocity, which should be -20 - 80kg x initial velocity, which should be 0? Please help I obviously am flawed somewhere in my logic.

I assume you meant "a 20 meter tall building", as I added above.

Your math appears to be correct. Not sure what you're having trouble with. Tom's momentum when he hits the net is indeed about 3200 kg m/s. After landing safely in the net, Tom steps gingerly out, his momentum having safely been reduced to 0, as we would hope (otherwise, he would have impacted with the pavement, or else gone flying back upward).

The second question comes from a box sliding up a ramp at a 30 degree angle attached to a pully system. What is the acceleration of a 20 kg box if a force of 100 newtons is applied? Supposedly the 100 newtons is amplified by 2 thus making 200 newtons pulling on the box in the upward direction. I thought the force acting on the pulley system would in fact distribute evenly and come to 50 newtons. This is the only part of the question I do not understand. Please help and thank you.

Are you sure there is not a pulley on the box? I don't see how else you have a doubling of force.

In any case, assuming you have 200 N pulling on the box, the acceleration is just what you get when you balance out the forces. The force pulling up the ramp is (apparently) 200 N. The force pulling down the ramp is the weight of the box times sin 30° (which is ½): (20 kg)(9.8 m/s²)(sin 30°) = 98 N. So there is a net force of 200 N - 98 N = 102 N up the ramp. Solving the force/acceleration equation for acceleration and putting in the numbers:

F = ma

a = F / m
= (102 N) / (20 kg)
= about 5 m/s²

 

[rinsterman12]

The question was what is the acceleration of the box if a force of 100 newtons is applied, as depicted in the ramp and pulley shown. I thought to move the box x that 2x of rope would needed to be pulled. I thought that since 2t the force would distribute evenly or 50 newtons, so from my logic w= 1/2f x 2d. The answer says that w= 2f x d. I guess since you are only pulling the box x that is why the force is amplified by 2?

 

[rinsterman12]

Tom does go flying back upward, i thought his initial momentum would be 1600 and final 1600. This is my math: 80(20- -20) which equals 3200. THey wanted the change in his momentum.

 

[BerkReviewTeach]

Tom does go flying back upward, i thought his initial momentum would be 1600 and final 1600. This is my math: 80(20- -20) which equals 3200. THey wanted the change in his momentum.

His speed at impact with the net would be around 20 m/s in the downward direction when starting at rest from 20 meters high. You are correct in all of your calculations, because his momentum on impact is -1600 (if we call down the negative direction) and exit momentum from the net has to be +1600 if you are correct about the change in momentum being +3200.

However, if you visualize this problem, Tom fell from a 20 meter building striking the net (which by the calculation must have been flat on the ground for Tom to fall the full 20 meters) and he had a perfectly elastic collision (retaining all of his kinetic energy). Be happy with your numerical processing on this question, but you should note that the MCAT questions are more realistic so that you can visualize what is happening and reason it out via intution. If you did that here, then you would conclude that collisions off of nets laid flat on cement are perfectly elastic, and because of the consequential perpetual motion associated with such a collision, Tom is still bouncing as you are reading this. Poor Tom, although it beats rolling a ball up hill for eternity, bouncing eternally from a fire safety net is still a bad curse for life.

 

[BerkReviewTeach]

The answer says that w= 2f x d. I guess since you are only pulling the box x that is why the force is amplified by 2?

That would depend on the pulley. The pulley they are showing must have two vertical ropes between the fixed end of the rope and the point where the rope leaves the pulley. This would generate a mechanical advantage of 2, amplifying the applied force double.

 

[rinsterman12]

thanks for the help