Forces: rope pulling bucket upward

[Maiia]

Hi, could someone look over my work and tell me what I'm doing wrong? I seem to be getting the wrong answer...

Homework Statement

A 4.7kg bucket of water is raised from a well by a rope. The acceleration of gravity is 9.81 m/s^2. If the upward acceleration of the bucket is 3.1 m/s^2, find the force exerted by the rope on the bucket of water. Answer in units of N.

The Attempt at a Solution

This is what I did:
1) I used F=ma , plugging in 4.7kg for m and 9.81 for a. I solved to get F= 46.107 N (force down)
2) I used F=ma again, plugging in 4.7kg for m and 3.1 for a. I solved to get F= 14.57 N. (force pulling up- at least part of it)
3) Because the forces must be equal and opposite, to get F normal (which I assume is the 2nd part of the force pulling the bucket up), I subtracted 14.57 from 46.107N to get Fnormal= 31.537 N

 

[PhanthomJay]

It is usually best to draw free body diagrams and examine the real (as opposed to pseudo) forces acting on the object, and then apply Newton 2. Newton 2 does not say F=ma, it says F_net =ma. The bucket's weight acts down, and the tension force acts up. Thus the net force is _________? Now solve for T using Newton 2.

 

[Maiia]

The net force is the total force, right? And what is T? There is no T in the Fnet=ma equation...?

 

[Maiia]

and is the normal force part of the net force? i assumed it was.

 

[PhanthomJay]

The net force is the total force, right? And what is T? There is no T in the Fnet=ma equation...?

The force in the rope is what i called "T", representing Tension (T stands for tension). There is really no normal force in this problem when you draw the FBD of the water bucket and rope system. Normal forces typically 'push toward ' an an object, whereas tension forces 'pull away' from the object. And yes, net force, total force, sum of forces, or unbalanced force, are generally synonymous terms.

 

[Maiia]

ok, so if i add the two forces, I get a net force of 31.537N. But that is a force upward. It asks for the force the rope exerts on the bucket..wouldn't this be 2 reaction pairs? the gravity and applied force then the tension and the force opposite from tension? sorry I'm really confused...I just learned this stuff today...

 

[Maiia]

oh wait i think i figured it out- so the tension of the rope pulling on the bucket has to be greater than the force of gravity for the bucket to be moving upward...so you add the the force of gravity and the force from multiplying acc upward and mass, right? to get the total force for the tension.

 

[PhanthomJay]

Newton 3 talks about action/reaction force pairs, each of which pair acts on different objects (the rope tension exerts an upward force on the bucket, and the bucket exerts a downward force on the rope, for example). But we're talking Newton 2 here, which addresses forces acting on the same object. So isolate the bucket and look at the forces acting on it. The weight, mg, or 46N as you noted, acts down on it. The tension or pulling force in the rope acts up on it; it is unknown, just call it "T". Since the bucket accelerates up, T must be greater than mg, and the total or net force, which is T-mg, must act up, in the direction of the acceleration. Now solve for T using F_net=ma.

 

[PhanthomJay]

oh wait i think i figured it out- so the tension of the rope pulling on the bucket has to be greater than the force of gravity for the bucket to be moving upward...so you add the the force of gravity and the force from multiplying acc upward and mass, right? to get the total force for the tension.

Well, yes, that should get you the right answer, but show your work.

 

[Maiia]

Thanks so much for your help :)