Physics Help (energy)

[boxcarracer767]

I am stuck on this problem dealing with energy, and I am having trouble with understanding the formulas.

A ball with a mass of M is on a frictionless curved track with a radius of R. The track sits atop a table that has height of H. Solve the following in terms of R,g,H, and M.
a) the velocity of the ball
b) the time it takes to hit the floor
c) the distance D the ball lands from the base of the table
d)the total amount of energy the ball has when it strikes the floor

Here are my answers, are these correct
Would I also need to include the radius of the curve to the measure of velocity?
a) v= sqrt(2gH) ???
b) t=sqrt(2gh)/r ???
c)???
d) would i add 1/2mv^2 + MgR+MgH ???


Thanks

[j4ck]

It is hard to answer this question without a diagram to look at...and I don't want to guess at exactly what is going on. Instead, I'll just give you a bit of a hint:

You are dealing with conservation of energy in part a). How much potental energy has the ball lost once it gets to the point where you must calculate it's velocity? You know this potential energy must have transformed into kinetic energy.

For part b) you need to remember that the ball's motion in the x direction does not effect it's motion in the y direction. How long would it take the ball to reach the ground while in free fall?

Part c)...it's all projectile motion, baby. You need to know the ball's velocity in the x direction immediately after it leaves the table. You will probably want to use your answer from b), as well.

Part d): Better rethink your answer on this one. Remember, the ball always has the energy it started with...just the FORM of that energy has changed.

[timbit]

ok, its' been a few years since physics 12 lol, but i'll see if i can help a little, since no one else has replied...

for c: distance = v(at the end of track) x t(time it takes to hit floor)

for a and b: i have absolutely no clue, probably because i don't have a picture (for some reason, i found pictures vital in physics). i will say that the answers don't look right to me, but again, that's just a guess.

for d: i would try to split it into two steps... solve for energy at the end of the track (should not be a prob if you get the other three) and add it to the energy gained in the fall to the floor. edit: j4ck is way better on this one. my way sucks after seeing his lol.

just out of curiosity, what grade is this?
oh yeah, this is no substitute for asking questions in class, and i take no responsibility for the rightness or wrongness of these suggestions, lol.

[discodanman45]

Hey, I totally missed ths post! My Master's degree could have been handy here j4ck is totally correct on his explanation without knowing some information. It is unclear what happens before the ball leves the table. It seems that the ball is released from the inside of a curved track exactly at the middle of the track. So the initial PE (potential energy) would be MgR + MgH. This is the total energy of the system.

for a) I believe you mean the velocity of the ball when it leaves the table. This can be solved from v = sqrt (2gR).

for b) remember Galileo's superposition principle that you treat the horizontal and vertical movements independent of each other. Basically you know initial velocity = 0, acceleration in vertical direction is g, and the height it falls is H. You know three things so you can solve for both the time and final velocity. Use the equation H = vt + (1/2) g t^2. Where v = intial velocity. Therfeore t =sqrt (2 H /g)

for c) remeber that the horizontal velocity never changes so v = x / t. So the distance x it goes is just given by x = v t, where v is from part a) and t is from part b)

for d) the total amount of energy when the ball hits the floor is just the initial PE with respect to the floor. PE = MgR + MgH = Mg (R + H)

I am guessing at the initial positionof the ball, but I have seen similar problems to the one you needed help with. Good luck in your class!