A smooth massless wedge is pushed by a horizontal Force P....

[Shivam]

Homework Statement

A smooth massless wedge is pushed by a horizontal Force P, then
(1) If P=0, than N<mgcos(theta); N=Normal reaction received by block
(2) If P>0, than N=mgcos(theta)
(3) If a=0, than N=mgcos(theta);a=acceleration of the wedge
(4)If P=mgtan(theta), than N=mg/cos(theta)

Relevant Equations

F=ma, Cpmponents of weight

Answers- 1,3,4

My attempt, the wedge being massless, there shoul not be any force acting on as it will then have infinite acceleration, so by that i really can't think of how force is applied on pully.

 

[haruspex]

the wedge being massless, there shoul not be any force acting on

No net force.

 

[Shivam]

No net force.

Can you help, in first option N<mgcos(theta) but if there is even a little bit of Normal force on wedge that how can it be true(the option is correct) ?... If you can explain the 1,3,4 option then please help me

 

[BvU]

As Haruspex said, no net force. P is not the only force working on the block.
Can you describe what you think will happen when P = 0 ?

 

[Shivam]

As Haruspex said, no net force. P is not the only force working on the block.
Can you describe what you think will happen when P = 0 ?

There is only two force acting on the block .. one is p which is zero here and the other is normal reaction between wedge and block also the the normal due to ground on wedge is also zero, so only force acting is normal reaction but how will it be balanced by and by whom. That's all is could I think of

 

[BvU]

What about the force mass m exerts on the wedge ?

 

[Shivam]

What about the force mass m exerts on the wedge ?

the force mass m exerts is the Normal reaction between them. The mg will have two component mgcos(theta) and mgSin(theta), the mgSin(theta) is just parallel to inclined surface so it will not affect the wedge, the mgCos(theta) is pushing on the wedge, so what's next

 

[haruspex]

the normal due to ground on wedge is also zero

Why do you think that?

 

[Shivam]

Why do you think that?

ok, it won't be, let me try drawing FBD.

 

[Shivam]

What to do next I can't figure it out...

 

[haruspex]

View attachment 245688What to do next I can't figure it out...

Since you have now omitted P I assume you are thinking of (1).
The normal force between block and wedge might not be mg cos θ in this case.

For the net force on the wedge to be zero, what must the two normal forces on it be?

 

[Shivam]

Since you have now omitted P I assume you are thinking of (1).
The normal force between block and wedge might not be mg cos θ in this case.

For the net force on the wedge to be zero, what must the two normal forces on it be?

Let's think of this, even if N1 <mgCos(theta) then let's make it's components one will be in horizontal and one will be in vertical and the vertical component of N1 will be canceled by the Ng given by the ground, then what will cancel horizontal component. ?

 

[Shivam]

(1.)Let's think of this, even if N1 <mgCos(theta) then let's make it's components one will be in horizontal and one will be in vertical and the vertical component of N1 will be canceled by the Ng given by the ground, then what will cancel horizontal component. ?

(2.) Another thought of mine is, wedge is massless, so it doesn't even exist then the block should only move in downward direction with mg force then N1 should be equal to zero

 

[haruspex]

ok, it won't be, let me try drawing FBD.

It won't be in general. It could be in some cases. I'm not sure which of 1 to 4 you have in mind.

 

[Shivam]

It won't be in general. It could be in some cases.

Can you please explain the answer, I have been stuck with this for 3 days now, 2 days I thought about it myself and then yesterday I posted this question

 

[haruspex]

then what will cancel horizontal component. ?

Clearly, nothing.. so what do you deduce about the normal forces on the wedge when P=0?

 

[ehild]

(2.) Another thought of mine is, wedge is massless, so it doesn't even exist then the block should only move in downward direction with mg force then N1 should be equal to zero

That is correct... If P=0, there is no horizontal external force on the system, the centre of mass does not move in horizontal direction: but the wedge is massless, the centre of mass is in the block. The block moves down the slope, and the wedge moves to the left and that motion cancels the horizontal component of motion of the block along the wedge. No horizontal acceleration of the block, no force in that direction...

 

[haruspex]

That is correct... If P=0, there is no horizontal external force on the system, the centre of mass does not move in horizontal direction: but the wedge is massless, the centre of mass is in the block. The block moves down the slope, and the wedge moves to the left and that motion cancels the horizontal component of motion of the block along the wedge. No horizontal acceleration of the block, no force in that direction...

Yes, if P=0, but I took the prefix (2) in @Shivam 's post #13 as referring to case 2 in post #1.