Dynamics question

  • #1
Plutonium88
174
0

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.
 
Last edited:

Answers and Replies

  • #2
nasu
3,957
582
The small mass accelerates along the y direction. So Fnet is not zero along this direction.
 
  • #3
Plutonium88
174
0
Ahh I see..
Fnety=zg=FN-zgcosA
FN=2zg/cosA

Ans; 2zgtanA/(z+P)
 
  • #4
nasu
3,957
582
The vertical acceleration of the small object is not g. It's not falling freely.
 
  • #5
Plutonium88
174
0
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.
 
  • #6
nasu
3,957
582
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.
 

Suggested for: Dynamics question

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
0
Views
867
Top