# Tension in rope pulling up a bucket. Thanks

## Homework Statement

"A pail is suspended from a vertical rope, wrapped around a winch, so that the pail can be raised or lowered inside a well.

The weight of the emply pail is 4 N. Suppose the pail is descending vertically with increasing speed. Is the tension in the rope larger than, smaller than, or equal to 4 N? Explain?

## The Attempt at a Solution

I cannt find the reasoning in my text book for this. Can anyone point me in the right direction? Any help would be great!

May I suggest you draw a free body diagram for the bucket when it is at rest. from there you should be able to figure out the reasoning

So I drew a FBD...

There is a force of Gravity(Fg) acting on it, pulling it down.

There is a force of tension(Ft) acting on it, pulling it up, or keeping it in balance.

The pail weighs 4N - And since the pail if descending, the force of Gravity(Fg) is greater.

First off, is what I said above correct?

Since its descending, would the tension be the same? Why?

Thanks!

gneill
Mentor
The pail weighs 4N - And since the pail if descending, the force of Gravity(Fg) is greater.

That's not correct. The force of gravity is independent of the motion. It depends only upon the masses that are mutually attracting each other.

Sometimes it's helpful to imagine taking situations to their extremes (as a thought experiment). In this case, suppose that the rope were being paid out at a rate that allowed the bucket to fall with its maximum acceleration. That is, g. The bucket would essentially be in free-fall. What would be the tension in the rope in such a case?

That's not correct. The force of gravity is independent of the motion. It depends only upon the masses that are mutually attracting each other.

Sometimes it's helpful to imagine taking situations to their extremes (as a thought experiment). In this case, suppose that the rope were being paid out at a rate that allowed the bucket to fall with its maximum acceleration. That is, g. The bucket would essentially be in free-fall. What would be the tension in the rope in such a case?

Oh...

So, the tension of the rope would be less than 4 N ?

I dont quite understand why the force of gravity is not greater? If it was stationary, that means that the rope holding it and gravity are in balance, like a book on a table.?

Since its falling, would gravity not be larger?

I can see now though that the tension would be in fact lower - Is that correct?

Oh...

So, the tension of the rope would be less than 4 N ?

I dont quite understand why the force of gravity is not greater? If it was stationary, that means that the rope holding it and gravity are in balance, like a book on a table.?

Since its falling, would gravity not be larger?

I can see now though that the tension would be in fact lower - Is that correct?

Yes the force of gravity on a mass is constant regardless of motion, if its accelerating it simply means the other forces acting on the object do not fully counterbalance the force of gravity so in this case T<Fg so its accelerating

gneill
Mentor
Oh...

So, the tension of the rope would be less than 4 N ?

I dont quite understand why the force of gravity is not greater? If it was stationary, that means that the rope holding it and gravity are in balance, like a book on a table.?

Since its falling, would gravity not be larger?
Nope. The force of gravity would be the same. What is less is the force that was holding it from falling! Don't confuse force with motion! If you have two forces that are balanced and holding something stationary and one of those forces is removed, the remaining force didn't become stronger; it simply became unopposed.
I can see now though that the tension would be in fact lower - Is that correct?

That is correct.

vela
Staff Emeritus
Homework Helper
The pail weighs 4N - And since the pail if descending, the force of Gravity(Fg) is greater.
Greater than what?

The word descending tells you about the direction the pail is moving; that is, it tells you the way the velocity vector is pointing. However, it doesn't really tell you anything about the direction of the net force on the pail. If this doesn't make sense to you, think about a ball thrown straight up. Half the time, it's ascending; the remaining time, it's descending. Yet the entire time, gravity pulls down on the ball. So you can see the direction of the velocity vector and the direction of the force aren't always the same.

Nope. The force of gravity would be the same. What is less is the force that was holding it from falling! Don't confuse force with motion! If you have two forces that are balanced and holding something stationary and one of those forces is removed, the remaining force didn't become stronger; it simply became unopposed.

That is correct.

Yes! gotcha!

So my free body diagram would be just Fg and Ft correct? And the Ft arrow would be smaller, since it is falling.

This is not apart of the question, but im sure it will come up. Lets says the bucket is full of water and now weighs 20N, and now is pulled up at constant speed.

The tension in the rope would be equal to 20 N correct? Why?

gneill
Mentor
Yes! gotcha!

So my free body diagram would be just Fg and Ft correct? And the Ft arrow would be smaller, since it is falling.

This is not apart of the question, but im sure it will come up. Lets says the bucket is full of water and now weighs 20N, and now is pulled up at constant speed.

The tension in the rope would be equal to 20 N correct? Why?

Newton's first law -- if velocity is constant then no net forces are acting; the forces must be balanced, equal and opposite. The rope tension must balance the weight.

Newton's first law -- if velocity is constant then no net forces are acting; the forces must be balanced, equal and opposite. The rope tension must balance the weight.

oh I see...so yea it would be equal to 20 N then...

What do you mean by opposite?

gneill
Mentor
oh I see...so yea it would be equal to 20 N then...

What do you mean by opposite?

Opposite, as in directly opposed, in opposite directions.