A 14.0-kg bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant. What is the acceleration of the bucket? Is it up or down?
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This is Giancoli Answers with Mr. Dychko. The force of tension upwards on this bucket is 163 Newtons and the force downwards due to gravity is mass times the gravitational field strength, 9.8 Newtons per kilogram. Let's multiply that by 14 kilograms, it gives 137.2 Newtons downwards. The net force in the bucket is the tension upwards minus the gravity down, that equals mass times acceleration that's a 163 minus 137.2 Newtons, equals mass times acceleration and we'll divide both sides by m to solve for a the acceleration. And we have 163 minus 137.2 all divided by 14 kilograms, that gives 1.84 m/s squared upwards, and that's positive, that's how we know it's up. Then we can also look at the diagram and see that the force upwards is greater than the force downwards. And the acceleration has to go in the direction of the greatest amount of force.
Why is acceleration upward if the problem says the bucket was lowered?
Hi callie, thank you for the great question. Acceleration and the direction of motion are not always the same. When they're different, that's when something is slowing down. Even though the bucket is moving down, the upward acceleration means its downward velocity is slowing. To picture this concept with a different example, consider a ball thrown up in the air - it's initially moving upward, but we know the acceleration is down since the only force (neglecting air drag) is due to gravity downwards. Its acceleration is down, in other words, even while it is moving up.
All the best,
Shaun
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