Block Moving Down A Moving Wedge

[GnG.Vike13]

Homework Statement

A mass of 5kg and wedge of 10kg are held at rest. All surfaces are frictionless. No outside forces are acting on the system. θ of the wedge is 30°. Once the block and wedge are let go, what happens to both objects? What is the acceleration of the block left/right and what is the acceleration of the block down the wedge?

Homework Equations

I seriously do not get this problem at all.

The Attempt at a Solution

When I made a fbd, and split both masses into x and y components, it showed that the wedge will accelerate in the opposite direction of the block's acceleration.

Anyone understand this?

 

[Doc Al]

... anyone? I just don't why the block will continue to move along with the wedge if the wedge goes backwards.

Why not? The block slides down the wedge, pushing the wedge backwards. If you viewed their motion with respect to the ground, how would it look?

 

[GnG.Vike13]

Why not? The block slides down the wedge, pushing the wedge backwards. If you viewed their motion with respect to the ground, how would it look?

Thank you for the reply.

I understand that the block will continue to move down along the block... But we had a problem with this concerning conservation of energy. But the work that the block does on the wedge is positive and the work that the wedge does on the block is positive, why is energy conserved? It doesn't make sense.

 

[Doc Al]

Why doesn't it make sense? Don't forget about gravity.

 

[GnG.Vike13]

Because a positive work is acted on in the system. Therefore, energy must've been added to it.

 

[SammyS]

bump

Please, read the Forum rules regarding bumping.

 

[SammyS]

Have you looked at the links at the bottom of this web page. This problem has been addressed many times, sometimes quite well.

 

[Doc Al]

Because a positive work is acted on in the system. Therefore, energy must've been added to it.

Once again I will remind you not to forget about gravity.

Also you may want to compare what happens when the wedge cannot move versus when it is free to move (as in this case).

 

[GnG.Vike13]

I am taking gravity into account. The wedge moves left and the block moves right and down. There is a positive force to the left acting on the wedge and a positive force to the right acting on the block, along with gravity acting down. Therefore, all work done in this problem is positive. Since we area adding positive work into the system, Wnc= delta E

 

[Doc Al]

There is no non-conservative work being done here. The increase in KE of the block and wedge is due to the work done by gravity.

 

[GnG.Vike13]

So, the work done by gravity is shraed between the two objects, correct?

But looking at it from a Newton's Laws perspective, how would you go about solving for the accelerations of each objects? Like, how does the acceleration of the wesdge relate to the acceleration of the block?

 

[Doc Al]

So, the work done by gravity is shraed between the two objects, correct?

Right.

But looking at it from a Newton's Laws perspective, how would you go about solving for the accelerations of each objects? Like, how does the acceleration of the wesdge relate to the acceleration of the block?

Start by identifying the forces acting on each object and draw yourself a FBD of each. (You might have already done that.)

One constraint to apply is that the block maintains contact with the wedge. Call the acceleration of the wedge a_w and the acceleration of the block with respect to the wedge a. (a_w will be horizontal and a will be parallel to the wedge.)

 

[SammyS]

Have you looked at the links at the bottom of this web page. This problem has been addressed many times, sometimes quite well.

Check these out !