Forces acting on an object -free body diagrams

[sgstudent]

Hi guys, I have a dyanamics question to ask. Thanks for the help!

In the scenario there is two objects-one the box and the hand pushing it

When i push an object, there will be a force acting on the object and hence a reaction force acting on my hand. So, if i were to apply 10N of force on a box i would also receive 10N of force acting on my hand. With just this 2 pieces of information in mind, would it be possible to tell what is the force acted on my hand (FBD of hand) to counteract the 10N reaction force?

Or will the minimum force exerted by my hand equal to the force that i exert on the box meaning 10N of force such that they counteract each other so net force of hand is 0N - or will the force i exert on my hand be 20N such that the net forces of both objects must be equal (if 20N of force exerted on hand net force=20N-10N=10N and on the box, net force=10N of force exerted on the box)? So, is there a rule to follow, like will the two bodies have the same net force, or same acceleration or is it up to me to exert the force on my hand to counteract the box just that i must have a force that is equal to the force exerted on the object itself (or else i will have an opposite net force which probably doesn't work).

I'm unsure about this as there are two bodies to consider and I don't know how to determine the forces of the two object. Thanks for the help!

 

[chrisbaird]

If you were in floating in space, and you pushed a box with 10N, it pushes back on you with 10N, and you both fly off in opposite directions, accelerating under this force pair. There are no other forces. What you probably have in mind is standing on the ground pushing on a box. In that case (unless you are standing on ice), you push with 10N on the box and the box pushes back with 10N on you, but you don't accelerate because the ground is in the way. More exactly, your foot pushes the ground with 10N and the ground pushes on you with 10N. The Earth experiences a net 10N, but it is so massive that its acceleration is to small that it is essentially zero. You experience a net 0N, 10 from the box in one direction and 10 from the ground in the opposite direction, so that your acceleration is zero. The box experiences a net 10N and accelerates away from you (assuming the friction between box and ground in negligible).

 

[chrisbaird]

Forces describe the interaction between two objects. For mechanical forces, these exist at the point of contact. On the other hand, accelerations describe the objects themselves. Newton's law is more clearly written as F_{total on a body} = m_body a_body.

 

[sgstudent]

Oh the the net forces on the hand will be up to the setter? Like how much force I exert to counteract it or not counteract it at all like in the space example you gave? Thanks for the help!