Solve Acceleration of Inclined Plane Given z,P,A

[Plutonium88]

Homework Statement

a mass z is held on an incline plane with mass P. when the the masses are released, both objects begin to move and accelerate. find accell of the incline plane

GIVEN: z,P,angle A, surfaces are frictionless

solve in terms of these variables.

Homework Equations

f=ma

The Attempt at a Solution

i chose my positive x direction along the ground surface below the incline plane, toward the direction of its motion.

so first i solved for the small mass on top the normal force, which is the force which applied onto the incline plane by the small mass.

fnety=0=FNcosA - zg
FN= zg/cosA

now when i do the FBD of the incline plane the forces acting on it, are the normal (FN) which gives it an unbalanced force in the +X direction.

so i get the expression

fnetx= (z+P)a=FNsinA

subbing in the FN,i get

a= zgtanA/(z+P)

is this correct? if not can you tell me where i am going wrong.

 

[nasu]

The small mass accelerates along the y direction. So Fnet is not zero along this direction.

 

[Plutonium88]

Ahh I see..
Fnety=zg=FN-zgcosA
FN=2zg/cosA

Ans; 2zgtanA/(z+P)

 

[nasu]

The vertical acceleration of the small object is not g. It's not falling freely.

 

[Plutonium88]

The vertical acceleration of the small object is not g. It's not falling freely.

would it make it more simple if i chose a different frame of reference.

 

[nasu]

You could work in the non-inertial frame of the moving inclined plane. But I am not sure it makes simpler. Depends how it is easier to visualize for you. In the inertial frame attached to the ground or in the moving frame.