Forces and Inclined plane (ramp)

[homo-sapiens]

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]

 

[homo-sapiens]

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?

 

[mfb]

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).

 

[homo-sapiens]

should I introduce kinematics equations into this problem?? or would I be able solve this problem with only Newton's three laws??

 

[Satvik Pandey]

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.

 

[homo-sapiens]

pseudo force? thanks. you will look into ot

 

[homo-sapiens]

i will look into it . sorry tablet typo

 

[Satvik Pandey]

i will look into it . sorry tablet typo

Ok. Please reply if you need help.

 

[homo-sapiens]

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.

 

[Satvik Pandey]

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.:)