Conservation of Momentum Question

[Anan275]

Does anyone know how do this question:
1. Student 1 pulls to the left with a horizontal force on a 60 kg crate on a smooth floor. Student 2 pulls to the right on the same crate with a force of 250 N at an angle of 40º above the horizontal. The crate starts from rest and when it has moved 20 m

it has a velocity of 4.2 m/s

. Find the work done by each student on the crate.​

 

[K^2]

I'm sure you are right, but the real world problems are a nightmare to understand. What about my diving spin. There's no friction there, but I spin in the direction I throw my arms. Also, if I just move my arms in that direction, my body goes in the other direction, and I don't spin at all. I was once told that it is 2 problems. First I twist in the direction I want to go .. it stops .. and then I go in that direction.

Like I said, rotation is way more complicated. Mass of an object cannot change, except by splitting into several objects. That's why you are so limited when dealing with conservation of momentum. Both total momentum and total mass of the system are fixed, so you can't do anything about velocity of the center of mass.

With rotation, the equivalent is the moment of inertia. And moment of inertia of a body depends on configuration. That's why your spin accelerates when you pull in the limbs. But it's also why you can turn your body seemingly by throwing your weight around. What you are really doing is turning one way and then another, but from different configuration, so as to have different moment of inertia. The result is a net rotation which could not be achieved otherwise.

I know it might feel this way, because this sort of movement is very intuitive to human brain, but you do a lot more than just throw your arms in a particular direction. Your entire body is involved in making that direction change.

 

[Simon Bridge]

@Anan275: that would be off-topic for this thread, which is about conservation of momentum. You should start a new thread for that question.

 

[Buckleymanor]

There are plenty of mechanisms I can build that demonstrate conservation of momentum. But it's been done before plenty of times. Showing an actual person get actual recoil from an actual bow, that would be kind of interesting. I don't really see how a crossbow on a skateboard would be any better than demos they show on air track.

I have had a look at air track and I am at loss to some of the explanations with regards to conservation of momentum and the mechanism in question( bow crossbow arrow string).
If you could point me towards an air track vid of the effect it would help.
In the meantime could you explain if it's an elastic, inalastic, or completely inelastic collision.
I go for the completely though I am not absolutely sure of my reasons and this is why the questions.

 

[K^2]

Huh. I can't find any videos of separation of two air track gliders either. I'll give it another look, but maybe that's something that needs to be set up.

Might be easier without an actual air track. We have some carts on rails for similar kind of demos over in the department. There is a pair of blue tooth accelerometers I can mount on them. And these carts have a spring release built into them with a very sensitive trigger. These things go off all the time when students do experiments with them. I can weigh one of the carts down, trigger the release and record accelerations and integrated velocity readings.

Collisions are related to recoil, of course. You can look at recoil as time-reversal of the inelastic collision. But for it to be a perfect analogy, the inelastic collision needs to be set up so that the combined motion after collision is zero. Or look at it from center of mass frame where that's guaranteed to be the case.

None of it is quite as impressive as firing a bow, though. I don't think anybody is surprised that when one cart pushes the other with a spring, it pushes itself in the opposite direction. With bow, more things are going on. There is reaction of string against the arrow, pull of the string on the limbs, acceleration of the limbs... And all of it adds up to exactly the same thing. That would be impressive to show.

By the way, if there are any other common physics experiments that people are talking about, but there doesn't seem to be footage of on YouTube, let me know. I can probably set it up at the department. They have a room full of equipment just for showing demos to students.