A 6kg bucket of water is being pulled straight up by a string at a constant spee

Question

A 6kg bucket of water is being pulled straight up by a string at a constant speed.

I determined that the tension on the string was

F = ma

F = (6kg * 9.8 m/s2) * 0a
F = 58.8 N

Now its asking

At a certain point the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now?

The correct answer was "about 78N"

I dont understand how this 78 N was calculated, my mass (6 * 9.8) stayed the same and a=3, so i would have figured it would be at least closer to (6 * 9.8) 3 = 176.4 N.

What am I missing?

Explanation / Answer

Your mistake is where you write F = (6kg * 9.8 m/s2) * 0a.

F=ma only works for F to F, which is the sum of the forces. Your T coincidently is correct because it comes from a similar formula, W=mg, which means you substituted 6kg for m and 9.8 m/s/s for a to find the T force, because it is equal to the weight.

The tension and weight are equal and therfor you got away with it at first because you have a F (the sum of all forces) where your acceleration is 0, meaning F (m*a) is 0. This makes opposite forces (the ones which subtract from one another), tension and weight, cancel eachother out and therefor they must be equal.

Basically what this means for your question is that at the bottom instead of multiplying by 3, you must add the new F to your T, which turns out to be 58.8+ ma = 58.8 +6*3= about 78 N.

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