Forces and Inclined plane (ramp)

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Homework Help Overview

The problem involves a block of mass m on a ramp of mass M, which is free to move, and the objective is to derive an expression for the acceleration of the ramp when both are released. The context is centered around forces acting on inclined planes and the application of Newton's laws.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the normal force acting on the block and its horizontal component, questioning the correctness of their calculations. Some suggest setting up forces for both the block and the ramp simultaneously to understand their motion better. There is also a consideration of whether to use kinematics or stick to Newton's laws, with references to pseudo forces and moving reference frames.

Discussion Status

The discussion has evolved with participants exploring different approaches, including the introduction of pseudo forces. Some have indicated they found a solution using this concept, while others express confusion about its definition and application.

Contextual Notes

Participants are navigating the complexities of the problem setup, including the absence of friction and the implications of the ramp's movement on the forces acting on the block. There is an ongoing exploration of the relationship between vertical and horizontal motions in this context.

homo-sapiens
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Homework Statement



A block of mass m is held in place on a ramp of mass M with a slope of angle θ, which in turn is held in place as shown in the figure below. The ramp is free to move on the surface beneath it. There is no friction anywhere. The block and the ramp are then released. Derive an expression for the magnitude of the acceleration of the ramp. (Use any variable or symbol stated above along with the following as necessary: g. Assume SI units.)

Homework Equations



f=ma[/B]

The Attempt at a Solution


[/B]
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since the ramp is pushing on the mass, the mass is also pushing back on the ramp with a force N (normal force). and to find the horizontal component of the normal force, I did sin0 times Force N. and force N = cos0mg. therefore i concluded the acceleration should be sin0*cos0*mg / M. But it's not correct, can someone explain this and tell me why?
 
The normal force will be different as the ramp is receding from the block (compared to the standard block-on-a-ramp problem).
You'll have to set up forces for both objects at the same time, and find a relation between the vertical and horizontal motion of the small block (it is not following the angle of the slope).
 
should I introduce kinematics equations into this problem?? or would I be able solve this problem with only Newton's three laws??
 
homo-sapiens said:
should I introduce kinematics equations into this problem?? or would I be able solve this problem with only Newton's three laws??
I think that this can be easily solved with Newton's three laws.Do you know the concept of pseudo force?
It will be easier to solve the problem by choosing a reference frame that is moving with the wedge.
 
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pseudo force? thanks. you will look into ot
 
i will look into it . sorry tablet typo
 
homo-sapiens said:
i will look into it . sorry tablet typo
Ok. Please reply if you need help.
 
ok, solved it by using pseudo force. Thank you so much for the tip. Still a bit confused on what pseudo force is but I will manage. Thank you again.
 
  • #10
homo-sapiens said:
ok, solved it by using pseudo force. Thank you so much for the tip. Still a bit confused on what pseudo force is but I will manage. Thank you again.
You are welcome.:)
 

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