Calculating the normal force with Newton's Laws

[abswors]

Homework Statement

Hey I could really use some help with this question. I know I need to use Newton's Laws but I am not sure if the force I am calculating when I us ethe equation F=ma is the right one. Please help:

Block A (of mass: mA = 500g) and block B (mB = 3kg) are placed in contact with each other on a frictionless surface. A force of 49.6 N is applied to block A pushing it into block B resulting in a normal force between the blocks. Calculate the strength of the normal force between block A and block B.

I would appreciate any help!

Relevant Equations

f=m*a
Here's what I have:

Block A is accelerating at a= 49.6/0.5 m/s (99.2m/s)
Block B force is F= 3kg * 99.2 = 297.6N
but I'm not sure where to go from here?

 

[Orodruin]

First of all, acceleration is measured in m/s^2, not in m/s. Getting units correct is very important.

Second, your first equation describes the acceleration of block A if the total force on A was 49.6 N. Is the pushing force the only force acting on A? Have you drawn free body diagrams for A and B?

 

[abswors]

Yes I have, sorry about the units error I wrote that very quickly. The pushing force is the only force acting on A in this system and I do have a free body diagrams. I am just not sure what information to use to find the normal force. I have attached the full question in case I left something out.

 

[haruspex]

The pushing force is the only force acting on A in this system

Then why does B move?

 

[abswors]

Then why does B move?

It moves because the two blocks are in contact, so there is a force.

 

[haruspex]

It moves because the two blocks are in contact, so there is a force.

Yes, A must be exerting a force on B, so what forces are acting on A?

 

[phinds]

Yes I have

No, you have not. You have shown a helpful graphic of the situation but that is not a FBD. Do you understand what a FBD is? You need to show all the forces in play.

 

[abswors]

Yes, A must be exerting a force on B, so what forces are acting on A?

That is what I am trying to calculate: the normal force between A and B

 

[haruspex]

That is what I am trying to calculate: the normal force between A and B

Ok, so we are agreed there are two forces acting on A, not just one as you wrote in post #3, yes?

Remember that you are free to choose subsystems. In the present problem, it will be convenient to start with the subsystem consisting of the pair of blocks. This allows you to ignore the normal force between them because it is internal to the subsystem. So now you have just one external force acting on the combined mass.

What does that tell you about the acceleration of this subsystem?

 

[Delta2]

Your "key mistake" as already pointed out but not emphasized is that the only force acting on A is the pushing force of 49.6N. There is one more force acting on A. Which one is it?
Once you take into account this force, then by applying Newton's 2nd law once for block A and once for block B you ll get a system of two equations with two unknowns: the normal force and the common acceleration of the blocks.
You will also need Newton's 3rd law to handle a small detail regarding the normal force (from block A to block B and from block B to block A).

 

[FactChecker]

You can calculate the acceleration of the combined A and B resulting from the total force applied. Then calculate how much of that force is required to accelerate B that much. That will be the force between A and B.

PS. If this helps you to get the solution, be sure that you understand how it can be methodically shown in a free body diagram.