Help Mike Find Velocity of Ball Down Incline - ME Dynamics Problem

[ChaosTheory]

I was wondering if anyone could help me out with this problem. Using the drawing attached, I have to find the velocity of the ball at the end of the incline, where the ball starts from rest. This isn't the whole problem, but this is what is giving the entire class (M.E. Dynamics) a major headache. Our professor can't even solve it. We keep finding more variables than equations. If possible, do it without DiffEqu.

Also, if you're interested, this problem is part of the project in R.C. Hibbeler's Engineering Mechanics: Dynamics (10th ed.) on page 94.

I appreciate any help you can give me.
Thanks,
Mike

 

[cepheid]

Is there friction in this problem?
Also,
Where is the specific difficulty?

 

[Doc Al]

Using the drawing attached, I have to find the velocity of the ball at the end of the incline, where the ball starts from rest. This isn't the whole problem, but this is what is giving the entire class (M.E. Dynamics) a major headache. Our professor can't even solve it.

A ball rolling down an incline and your professor can't solve it?? You must be leaving out some complication not obvious in the drawing.

State the problem exactly as given, and show us the work you've done on it.

 

[ChaosTheory]

This is what the problem says:
"Marbles roll of the production chute at 0.5 ft/s. Determine the range for the angle 0<=theta<=30 degrees for a selected position s for the placement of the hopper relative to the end of the chute." Refer to Fig 2

Because we're not sure how long the chute must be for 0.5ft/s (we calculated something very small, and changes with theta), our Professor just wants us to provide (x) along the chute, and (s) to get into the hopper within a range of Thetas.
We first need to calculate the acceleration to find the velocity at the end of the chute. We are ignoring friction.

Fy = m(a)y
Ncos() - w = m(a)y

Fx = m(a)x
Nsin() = m(a)x

The problem is there are 3 variables (N, ax, ay) and two equations. And yes, our Professor (first year teaching a lecture) cannot solve it.

I appologize for not knowing how to use the boards language for equations.

 

[Doc Al]

We first need to calculate the acceleration to find the velocity at the end of the chute. We are ignoring friction.



The problem is there are 3 variables (N, ax, ay) and two equations. And yes, our Professor (first year teaching a lecture) cannot solve it.

Consider the motion parallel to the plane. The only force on the marble is gravity. What's the component of the weight down the plane? Use Newton's 2nd law to find the acceleration.

PS: Your Professor must be pulling your leg!