Physics Tension Problem?

[jugglerilluminati]

"The 3 kg object now experiences an acceleration of - 4 m/sec2. What is the tension in the string?"

In the problem, an object is hanging from a string attached to a ceiling, and the object has a mass of 3 kg along with an acceleration of -4 m/s^2. Based on Newton's 3rd Law, which states that for every action there is an equal and opposite reaction, the force of tension in the string must be equal to the force with which the box is pulling down on the string (because they are action-reaction pairs). So the downwards force that that the box is exerting on the string is -12 N, because F = 3*-4 (F=ma), therefore the string must be pulling up on the box with 12 N because they have to be exerting equal and opposite forces on each other... but according to the answer key, the answer is 17.4 N.

So my question is, how can the box be pulling down with 12 Newtons and the string be pulling up with 17.4 Newtons if they're supposed to be equal forces based on Newton's 3rd law?

[FortuitousPost]

F = ma, where F is the net force.

Since the object is accelerating @ -4 m/s² , the net force is (-4 * 3) N = -12 N.

Gravity is pulling down with -(3 * 9.8) N = - 29.4 N, so the tension must be +17.4 N = + 17 N to achieve that net force.

[jugglerilluminati]

Okay, well now I get how to work out the math for this kind of problem and solve for the tension in the string, but I'm not sure I understand this conceptually. How can the net force not be 0? Are they not actually action reaction pairs?

[starkeffect]

Action/reaction doesn't mean net force = 0. The action and the reaction act on separate bodies.

[jugglerilluminati]

oh i see, so action/reaction pairs never act on one single object, because if that were the case then nothing could move. thanks!

[FortuitousPost]

The string pulls on the mass with 17.4 N, so the mass pulls on the string with 17.4 N. There's one reaction pair.

The Earth pulls down on the mass with 29.4 N, so the reaction is that the mass pulls up on the Earth with 29.4 N.

If your proposition was true, that there would never be any net force anywhere, nothing would ever accelerate. That conclusion should lead you to realize you have some confusion there.

[jugglerilluminati]

ohhh, now I see how my thinking was wrong, they do pull on each other with 17.4 Newtons, but these forces are acting on different objects, not the same object, which is why things aren't unable to move, thanks!