Solve Acceleration of Inclined Plane Given z,P,A

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In summary, the problem involves a mass z being held on an inclined plane with a mass P. When released, both objects accelerate and the question is to find the acceleration of the inclined plane. Using the given variables of z, P, and angle A, and assuming frictionless surfaces, the solution involves finding the normal force and using the equation f=ma to solve for the acceleration of the inclined plane. However, there is a discrepancy in the solution as the small mass does not accelerate at the rate of gravity. Working in a non-inertial frame attached to the moving inclined plane may make the problem easier to visualize.
  • #1
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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.
 
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  • #2
The small mass accelerates along the y direction. So Fnet is not zero along this direction.
 
  • #3
Ahh I see..
Fnety=zg=FN-zgcosA
FN=2zg/cosA

Ans; 2zgtanA/(z+P)
 
  • #4
The vertical acceleration of the small object is not g. It's not falling freely.
 
  • #5
nasu said:
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
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.
 

What is the formula for solving acceleration of an inclined plane?

The formula for solving acceleration of an inclined plane is a = g(sinθ - μcosθ), where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), θ is the angle of inclination, and μ is the coefficient of friction.

How do you find the acceleration of an inclined plane given the angle of inclination?

To find the acceleration of an inclined plane given the angle of inclination, simply plug the angle (in degrees) into the formula a = g(sinθ - μcosθ) and solve for a.

What is the role of the coefficient of friction in solving for acceleration of an inclined plane?

The coefficient of friction, represented by μ, represents the amount of resistance or friction between the inclined plane and the object. It is a crucial factor in determining the acceleration of the object on the inclined plane.

Can the acceleration of an inclined plane be negative?

Yes, it is possible for the acceleration of an inclined plane to be negative. This occurs when the force of friction is greater than the force of gravity pulling the object down the incline. In this case, the object will either move backwards or slow down.

What are some real-life applications of solving for acceleration of an inclined plane?

Solving for acceleration of an inclined plane is important in various fields such as engineering, physics, and sports. It can be used to design ramps and roller coasters, determine the speed of objects sliding down a hill, and calculate the acceleration of athletes running on an inclined track.

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