Sudden impact

1. May 22, 2006

parallax1234

so here i am doing my physics homework. everythings fine, but then i get this whopper of a problem, which is for major marks, and i cant seem to solve it for some reason. here she is:

a ramp is setup on the edge of a table

a ball slides down this ramp and picks up speed. just as it leaves the ramp it hits a stationary ball, identical to the first, located at the very bottom of the ramp

the two balls collide and fall a certain distance to the floor below, hitting the ground at exactly the same time.

the balls land on the floor below:

one of the balls lands 30cm away from the bottom of the ramp; 32 degrees to the right of ramp

the other ball lands 33.25cm away from the bottom of the ramp; 43 degrees to the left of ramp

some things to remember:

-the height of the ramp, height of the table, time, weight/size of the balls are unknown, but constant
-a single ball going down the same ramp lands 47.6 cm away from the bottom of the ramp.

prove in the most efficient way that momentum is conserved.

2. May 22, 2006

Hootenanny

Staff Emeritus
Welcome to PF parallax,

Please show some intial thoughts or working. Consider intial momentum prior to the collision. You will also require equations of uniform motion. Think projectile motion.

~H

Last edited: May 22, 2006
3. May 22, 2006

parallax1234

momentum = mass * (time/distance)

therefore, initial momentum = m (t/0.476)

final momentum1 = m (t/.30) [32 degrees right]
final momentum2 = m (t/.3325) [43 degrees left]

using the cosine law i find total final momentum:

total final momentum^2: [m (t/.30)]^2 + [m (t/.3325)]^2 - 2[m (t/.30)][m (t/.3325)]cos85

using the above value i find the angle using sine law.

-i ignored the downward motion of the two balls, because t and m are constant.
-i assume that the momentum of the ball going down the ramp without colliding = total initial momentum
-i forgot to mention that this data was collected from an actual lab, so there's some momentum that was lost to friction from going down the ramp and from air resistance.

i am left with a really long equation with a bunch of unknown variables. am i safe to assume that i can just put in a value of 1 for m and t, since they are both constant, the momentum before and after will be the same regardless of what value i choose.

i will likely get a percentage difference of around 15% -5%, momentum is not fully conserved, but its ok because its in a real-world environment, but in an isolated system it would be 100% conservation of mass...

am i on the right track here?

Last edited: May 22, 2006
4. May 22, 2006

parallax1234

i am an idiot: speed = distance/time not time/distance

i also used 85 as the angle, instead of 105......

having fixed this, i seem to have the problem solved:

5. May 23, 2006

Hootenanny

Staff Emeritus
Your working appears correct, and I can't spot an glaring errors. Your percentage of conservation seems reasnable, so I would say yes you have solved it. And without any help! Well done

~H