# Incline force

1. Sep 24, 2014

### homo-sapiens

1. The problem statement, all variables and given/known data

The face of block M in the figure below is shaped like a semicircular bowl of radius R. A mass m is placed at the top-left corner of the bowl and then let go. Find the acceleration of block M relative to the surface it is sitting on when m is a distance of 0.8R from the bottom of the bowl. There is no friction between M and m, or between M and the surface on which it sits. (Use any variable or symbol stated above along with the following as necessary: g. Indicate the direction with the sign of your answer. Assume the +x-axis is to the right.)

http://puu.sh/bMIJx/03bb46a1d0.png [Broken]

2. Relevant equations

f=ma

3. The attempt at a solution
All i got so far, cannot figure out a way to solve for acceleration. I guess i am missing some equations but i just can't figure it out.
http://puu.sh/bMIMh/216e860f3a.png [Broken]

Last edited by a moderator: May 7, 2017
2. Sep 24, 2014

### BiGyElLoWhAt

What's the a in your equations? You have a $ma\text{sin}(\theta)$ term that I'm not seeing. So you have a block and a ball or whatever you wanna call it, and there's the earth. How many forces are being exerted on little m? I see 3 in you're equation, but that equation for some reason doesn't look all that useful.

I personally don't see any reason to use centripetal equations of motion for this. What are the forces exerted on big M in the x direction and what are the forces on M in the y direction? (also, the problem statement says take +x -> which implies an acceleration in Cartesian)

3. Sep 25, 2014

### ehild

The block is moving, better to use conservation laws - conservation of momentum and conservation of energy.

ehild

Last edited: Sep 25, 2014
4. Sep 25, 2014

### homo-sapiens

the masin(θ) is the pseudo force of small block with respect to the big M.
Also, i don't think conservation of energy and momentum is viable in this case, since the question stated "Use any variable or symbol stated above along with the following as necessary: g." i don't think i can just use Velocity out of nowhere.

5. Sep 25, 2014

### BiGyElLoWhAt

The magnitude is not normal, but the direction of the force on small m is most definitely normal. Sum the forces on big M, then there will be 1 force you need to look at the forces on little m.

6. Sep 25, 2014

### BiGyElLoWhAt

I should clarify not the net force.

7. Sep 25, 2014

### ehild

The acceleration of M is related to the acceleration of the small mass sliding down on it, how?

ehild

Last edited by a moderator: May 7, 2017