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A 6kg bucket of water is being pulled straight up by a string at a constant speed
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?
Expert Solution
OK, you were on the right track with both formulas but you wanted to add the accelerations; not multiply.
F = ma
F = (6kg*9.8m/s^2)*0m/s^2 = 0!!! Not 58.8N
F = 6kg*(9.8m/s^2 + 0m/s^2) = 58.8N
now the bucket starts accelerating, this adds to the regular gravity (it doesn't multiply the force; it adds to the acceleration)
F = 6kg*(9.8m/s^2 + 3m/s^2) = about 78N.
This is what you are used to. If you ride in an elevator you feel a little heavier when it starts to go up and a little lighter when it starts to go down. You don't feel three times heavier when it starts to go up, nor to you come off the floor when you start to go down.
Very impressed that you tried something and showed your work; those are signs of someone who will go far.
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