Dynamics help: Block on a wedge on an incline (frictionless surfaces)

[Pipsqueakalchemist]

Homework Statement:

Block B of mass 10-kg rests as shown on the upper surface of a 22-kg wedge A. Knowing that the system is released from rest and neglecting friction, determine (a) the acceleration of B, (b) the velocity of B relative to A at 0.5 s

Relevant Equations:

Newton’s 2nd law
Relative motion

So I’m having trouble with relative motion with moving inclines and I literally can’t find any help online and my prof does a lot of these problems. This is one of my homework problems, can anyone help me with it please.

 

[PeroK]

According to the homework guidelines, you have to give this your best shot. Put some energy into it!

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[Pipsqueakalchemist]

According to the homework guidelines, you have to give this your best shot. Put some energy into it!

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Well I’ve tried the problem before and I looked over the solutions but I don’t fully understand it. To be specific I know how to set up the FBD but I don’t how to apply the relative motion of the block and the incline.

 

[PeroK]

Try using energy, rather than forces.

 

[Pipsqueakalchemist]

Try using energy and momentum conservation, rather than forces.

But this for Newton’s 2nd law section so I have to use forces. Do you want to see the solutions and maybe you’ll understand better than me.

 

[Pipsqueakalchemist]

Wished I joined this forum sooner ,my midterm is in a few hours and I kinda just accepted that I’m screwed at this point. Hopefully I can understand this better for the exam 😓

 

[PeroK]

But this for Newton’s 2nd law section so I have to use forces. Do you want to see the solutions and maybe you’ll understand better than me.

The diagrams are hard to read. The idea is that you write down all the forces (obviously) then look for physical constraints: in this case the relationship between the motion of the small block and the large block. Then it's a case of solving the simultaneous equations.

The solution looks light on explanation and heavy on numbers to me.