Why is tension present in the rope?

[Churchill Tech]

These is my problem

Assuming the surface on which A rests is frictionless and there is no drag on either of the bodies as they move at common acceleration.

Correct me if I’m wrong, I think the bodies should have a common acceleration since they’re connected

Why does F? exist??, I know that F? is exerted on the body B such that the net force on B downwards is less than mg but what is causing this force?, Looks to me like this force is a pull on the string by A but I don’t think there is any force acting to the left of body A besides friction and drag which I have assumed to be non-existent.

I would be grateful on getting well explained answer...Help me guys.

 

[Chestermiller]

Even if there is no force pulling to the left on A, the force F is still necessary to accelerate A. (A is not in equilibrium).

Chet

 

[Doc Al]

Looks to me like this force is a pull on the string by A

Yes. Both A and B exert forces on the string equal to F.

but I don’t think there is any force acting to the left of body A besides friction and drag which I have assumed to be non-existent.

Why would you need a force to the left of A?

 

[russ_watters]

Inertia.

Which, by the way, you need to consider for both objects, not just A.

 

[sophiecentaur]

Perhaps the easiest way to approach this is to think in terms of the Force being mg and that this force acts on the combined mass m+m₂.

 

[Doc Al]

Perhaps the easiest way to approach this is to think in terms of the Force being mg and that this force acts on the combined mass m+m₂.

But that won't explain the tension in the string.

 

[sophiecentaur]

The tension would be there because the mass m₂ is being accelerated at the rate that was just calculated. F = mA again

 

[Chestermiller]

Suppose F is the tension in the string. Have you drawn free body diagrams on the two masses? Please write down the force balance equation you obtained from these free body diagrams for each of the masses.

Chet