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if a block of mass m lies on a wedge of mass M,here all surfaces are smooth, and the block slips on the wedge, will the wedge have any acceleration?If yes, plz explain why and of what magnitude?

if a block of mass m lies on a wedge of mass M,here all surfaces are smooth, and the block slips on the wedge, will the wedge have any acceleration?If yes, plz explain why and of what magnitude?

Grade:12

3 Answers

Aman Bansal
592 Points
9 years ago

Dear Ashmitha,

Yes there will be an acceleration in the wedge dut to horizontal and vertical component of the block acceleration,

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vbhootna vb
14 Points
9 years ago
There is a acc. Tangical to the surface of wadge which gives the acc. To wedge and wedge starts motion and it mag. Is mgcosø/m = gcosø where ø is angle b/w horizontal and wedge
Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Ashmita,

 

Please note as all surfaces are smooth, there are no frictional forces anywhere.

So with that let's draw the force diagram for the combined system of the "Block and the Wedge"

 

Now for the Wedge, lets resolve the forces in Horizontal and Vertical Direction.

N2 (is already upwards)

Mg (is downwards), so we need to resolve only the contact force N1(that is exerted by the block on the wedge) into the horizontal component and vertical component.

Horizontal = N1sinx (towards the left)

Vertical = N1cosx (downwards).

 

Note that, there is only this horizontal component of the force that acts on the Wedge.

And hence this wedge would accelerate towards the left.

 

In the vertical direction, the forces would get balanced (as it is clear that the wedge cannot accelerate in the vertical direction).

So Mg+N1cosx = N2.

 

Hope that helps.

 

Also hope that you understood the concepts for the question on Newton's laws and pulleys, you'd posted on the forum.

 

All the best.

Regards,

Ashwin (IIT Madras).

 

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