Calculating Acceleration on an Inclined Ramp with Two Sliding Packages

[iHate Physics]

Homework Statement

Two packages at UPS start sliding down the 20 degree ramp shown in the figure. Package A has a mass of 7.00 kg and a coefficient of kinetic friction of 0.180. Package B has a mass of 12.0 kg and a coefficient of kinetic friction of 0.150.

How long does it take package A to reach the bottom?

http://img362.imageshack.us/img362/1479/knightfigure0825pe6.th.jpg

Homework Equations

F=ma (sorry but that's all I know for this question)

The Attempt at a Solution

I hate incline problems with a passion, and I have no idea how to start one. All I have done is draw free body diagrams for this question. I know you are supposed to apply Newton's second law, but it get confused when i do this on an incline question

 

[Saladsamurai]

On your free body diagram, if you take the incline as your x-axis, this should help simplify things.

 

[bob1182006]

can you show us what you got for Newton's second law when applied to each block individually?

For this problem you should first find the acceleration of package A. From there you can work out the time it takes to fall down the 2m @ 20* incline.

 

[iHate Physics]

k well for box A i got

Fnet = F B on A - Ff

and for Box B i got

F net = -F a on B - Ff

but what would F b on a be equal to if i broke it down into f=ma format? Would it be f= mass of b times the acceleration of b?

 

[bob1182006]

your missing the acceleration due to gravity in your equations.

and yes the force B exerts on A will be the net force that B is experiencing.

 

[iHate Physics]

oh crud i forgot, it should be Fgx in both questions.

 

[iHate Physics]

so i should work with diagram b right? to find the acceleration of block a.

 

[bob1182006]

it doesn't matter which one you work from, they both experience the same acceleration.
And since you need to substitute in force of block a on b, or force of block b on a. Eventually you will get down to the same equation with the same answer.

 

[iHate Physics]

k but like what do you mean substitute?

 

[iHate Physics]

i got 4.3586 as my acceleration..

 

[bob1182006]

could you show the work please? I got something like lower than your value for acceleration.

When you have the 2 formulas for the net force of A and B you need to consider the effect that B has on A because A has a higher coefficient of friction it will probably be slowing down B so B will be pushing down on A and thus giving it a bit higher acceleration.