AP Mechanics

fizman

post discussion for problem 2 here

jeffiziks

this is what i meant to say -

conservation of energy and conservation of momentum are both involved in this problem, as well as torque...i think

jeffiziks

I cant edit or delete my comments, okay here is the real one...

jeffiziks

conservation of energy and conservation of momentum are both involved in this problem, as well as torque...i think

jeffiziks

conservation of energy and conservation of momentum are both involved in this problem, as well as torque...i think

fizman

well, i think you made your point. you're right of course. energy and momentum are always conserved.

tell us a little more about conservation of momentum. how do you find it before and after the collision?

and where does conservation of energy apply? given necessary info, what could we predict using conservation of energy?

ihopeimnotwrongagain

i'm assuming no friction?
for momentum Pa=Pb
Pa=angular+linear(both for ball)
Pb=angularball+angularrod+linearball
with energy you clould predict V, a, x traveled, max rad. (rod), and time untill rest (rod). theres prob lots more but i can't think of them now

chelsealane

conservation of energy.

conservation of momentum
Pb=Pa

woooh graphics!

chelsealane

conservation of energy.

conservation of momentum
Pb=Pa

woooh graphics!

highdude420310

The momentum in the collision is conserved. I think an elastic collision happens but it kind of looks inelastic. The total momentum of the collision is at all times equal to the initial momentum of the ball. Using conservation of energy one could calculate the velocity of the ball and block after the collision, how far the ball travels, how long it takes the ball and block to stop.

fizman

conservation of momentum is true but difficult due to rotation. unless otherwise stated, collisions are inelastic meaning energy is not conserved. the rotation should suggest a rotational concept ie. angular momentum. the big question is this: how do you calculate the angular momentum before the collision? what would you need to know?

maybe a bit deeper look at what you mean, swmbo.

6strikekickball

to find the angular momentum of the ball right before it hits the long blue object couldn't you use the length of the blue object as the radius when finding moment of inertia

saveferris

to find the balls angular momentum you would need to know how fast its rolling and its radius. with the radius you could find its moment of inertia and from there with its angular velocity find its angular momentum. its angular plus its linear would give the ball's total momentum and that's what would be used in a conservation of momentum equation

fizman

6strike is right, you could use the length of the blue thing as the radius or at least the distance from pivot to where the ball hits the blue thing.

ferris, the ball is not rolling. it only has angular momentum due to its mass, velocity and shortest distance to the pivot which happens at impact.

QUESTION: how does the angular momentum of the ball change as a result of the collision? what would you need to know to solve for its, the balls, angular momentum after it collides?

zaggle56

Sorry i haven't blogged yet, but here's what i've got.

some or the angular momentum of the ball is going to transfered to the pendulum because the ball keeps moving after the collision. If the ball had stopped, all of the balls momentum and kinetic energy would have been transfered.To find the change in the angular momentum of the ball you would use the closest approach, that is perpendicular to some arbitrary point; i used the pivot point of the pendulum both times. since the radius changed during collision that is how you would find the change in angular momentum. :)

fizman

yes! also, the ball would slow down due to the collision. this too decreases its angular momentum. L=mvr for the ball.

fizman

here's the problem:
mass of ball = 500g
I of bat = .25kgmm
initial v = 4m/s
final v = 2m/s
length of bat = 60cm
deflection angle = 30 degrees
find:
(a)initial angular velocity of the bat after the collision
(b)maximum angle of rotation of the bat