Question

Question

Answer 1

Suppose you push on a box with a force F. The box applies a contrary force back on your hand. Translational equilibrium is achieved when the sum of the forces acting are zero. Why then does the box accelerate?

Answer 2

Because the two named forces applies to two different objects.
The force from your hand on the box accelerates the box and the force from the box on your hand acts on your hand and not the box.

Answer 3

And if the box weren't able to provide an equal magnitude back on my hand the box would break?

Answer 4

Yes, that would be right. Your hand would then accelerate into the box.

Answer 5

When you apply a force to a box, the resistive force results from the friction between the surface of the box and the surface of the floor. What is the resistive force when the floor is frictionless?

Answer 6

The box has inertia and will counteract all applied forces with a normal force at the point of contact.

Answer 7

So it would have the same result as if the surface weren't there?

Answer 8

Not really, think of it like this. You push on the box, the box pushes back on you. The box is in contact with the surface and if we have friction will push on it (tangent to the surface), and the surface will push back on the box.
If the force we applied is very small, the friction forces at the surface may completely counteract your pushing and it will stay put. But if you increase the force more and more there comes a point where the friction forces can't keep up and it starts to slide.
If we don't have any friction, it will just start to glide directly and keep on going. But we still have to push it to get it moving because of the inertia of the box.
Do you understand?

Answer 9

Yes. But isn't that the same as if there were a box in space? When we applied a force to the box the inertia would still resist acceleration.

Answer 10

Yes, it is the same except it may be "locked" to the surface by gravitational pull.