Momentum Question

[collegelife101]

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Two red blood cells collide each from 60° off the larger vein’s longitudinal axis at 10–1 m/s. What is the component of their final velocity along the longitudinal axis?

Solution:
Because the cells will have comparable masses, and the same initial velocities in the axis in question, they will have the same final velocity in that direction. Do not concern yourself with the other axis. Find the component of the initial velocities along the axis, v0 cos 60° = ½ v0, and that is the final velocity component as well. Using sine will lead to choice B. Using just one or two of the total initial velocity would be choices C or D.

I understand the math but am confused regarding the concept behind the problem. How do we know that the final velocity will be the same as the initial velocity in this case? Also, how can we assume that the final velocity will be the same for both masses? Sorry if this is a dumb question...I just really don't get physics.

 

[DrknoSDN]

The problem is saying that the components of both initial velocities pointing towards each other cancel out. So you then just have to add each of the components in the final direction.

The cos 60° = ½ part is explaining that each cell will contribute half of it's initial velocity to the final velocity. And since you have 2 cells moving at the same initial velocity you have (2 * 0.5) as your final value, so the final velocity = initial velocities.

If they impacted at an angle other than 60° Vfinal would not equal Vinitial.

 

[pizza1994]

i dont get this question either....it still doesnt make sense to me

 

[DrknoSDN]

i dont get this question either....it still doesnt make sense to me

What part?

Visualize a large vein going from left to right (horizontal). Also there is a smaller venule that is 60 degrees above horizontal and different venule 60 degrees below horizontal. So it looks like 3 roads merging into one.

If you have a blood cell traveling down each venule they would have the same mass and initial speed but the velocity vectors are not pointing in the same direction. The problem is saying that when they collide it's completely inelastic because they are confined to the large vein so there is no net vertical movement after collision. So you can ignore vertical motion.

If you only consider the horizontal movement than you simply do m1v1 + m2v2 = mfvf
Assume mass of 1 for simplicity you would get 1*Vcos(60) + 1*Vcos(-60) = 2 * Vfinal

The final horizontal momentum is double both initial horizontal momentums because you add the horizontal momentum together. The mass is doubled because the cells collide and are moving together in the larger vein. So if you have double momentum and double mass. The velocity in the horizontal direction must be the same as it was for each cell before the collision.

 

[pizza1994]

What part?

Visualize a large vein going from left to right (horizontal). Also there is a smaller venule that is 60 degrees above horizontal and different venule 60 degrees below horizontal. So it looks like 3 roads merging into one.

If you have a blood cell traveling down each venule they would have the same mass and initial speed but the velocity vectors are not pointing in the same direction. The problem is saying that when they collide it's completely inelastic because they are confined to the large vein so there is no net vertical movement after collision. So you can ignore vertical motion.

If you only consider the horizontal movement than you simply do m1v1 + m2v2 = mfvf
Assume mass of 1 for simplicity you would get 1*Vcos(60) + 1*Vcos(-60) = 2 * Vfinal

The final horizontal momentum is double both initial horizontal momentums because you add the horizontal momentum together. The mass is doubled because the cells collide and are moving together in the larger vein. So if you have double momentum and double mass. The velocity in the horizontal direction must be the same as it was for each cell before the collision.

well yeah so each cell initally has a velocity of 0.1 m/s and then when they combine the velocity will double and o shouldnt it be 0.2 m/s as the answer and not 0.05 m/s?

 

[DrknoSDN]

well yeah so each cell initally has a velocity of 0.1 m/s and then when they combine the velocity will double and o shouldnt it be 0.2 m/s as the answer and not 0.05 m/s?

The initial velocity in the horizontal direction is only 0.05m/s. You find this by taking [ 0.1m/s * cos(60) ]
After they merge it is still 0.05m/s. because the momentum is double but so is mass. Therefore velocity remains 0.05 in the horizontal direction.

The velocity doesn't double. Visualize cars colliding instead of blood cells and you could see it more simply. If two cars have initial velocity of 100 mph with 50 mph in the west->east direction component. When they collide it would still be 50 mph west->east.
If the cars instantly speed up to 200 mph horizontal after the collision it would look very strange.