# Block, wedge and slope

1. Feb 25, 2009

### springo

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

http://img187.imageshack.us/img187/9476/dib.th.png [Broken]

mA = 22kg
mA = 10kg
No friction
At t = 0, at rest

a.- Find aB
b.- Find vB/A at t = 0.5s

2. Relevant equations

3. The attempt at a solution

http://img504.imageshack.us/img504/3786/dib3.th.png [Broken] http://img504.imageshack.us/img504/9979/dib2.th.png [Broken]

I got to the following equations:
mA·aA = mA·g·cos(30) + NB·sin(50)
0 = NA - mA·g·sin(30) - NB·cos(50)

mB·aA·sin(30) = NB - mB·g·cos(20)
mB·aB/A - mB·aA·cos(50) = mB·g·sin(20)

There must be something wrong in these because after solving my results are wrong.
I don't know if I chose the wright base for studying each body (maybe the equations would be simpler with some other base?).

Thanks for your help!

Last edited by a moderator: May 4, 2017
2. Feb 25, 2009

### Sonolum

I'm having a little trouble figuring out how you got to those equations - can you tell me a little more of your reasoning?

3. Feb 25, 2009

### springo

I used Newton's 2nd law and then projected the vectors.

4. Feb 25, 2009

### Delphi51

It seems to me that you have oversimplified. For starters, the acceleration of block B is going to be partly vertical and partly horizontal. It will not be in the direction of the ramp surface because that surface is falling and moving to the left. I think you need both horizontal and vertical accelerations for both blocks.

I'm thinking of the free body diagrams for A and B. I can write sum of forces = ma in each direction for each block, and get 4 equations with 6 unknowns including the 4 accelerations and the two normal forces.

NBsin(20) = 10aBx horizontal
NBcos(20) - 10g = 10aBy vertical
-NBcos(20) - NAcos(60) = 22aAx horizontal
-NBsin20 - 22g + NBsin(60) = 22aAy

Block A can only accelerate along the ramp so aAy = aAx*tan(30)

Still missing one equation. Must be something to do with B accelerating along its ramp, but it is itself accelerating so awkward to write!

Last edited: Feb 25, 2009
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