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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14-10-2022
Physics

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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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charithran8975 charithran8975 · Answer 1 · 2022-10-20T04:03:34-04:00

A 14.0-kg bucket is vertically dropped by a rope with 163 n of tension at any given time. The acceleration of the bucket is upward-directed and has a value of 2.06 ms^-2.

Let's imagine that two bodies are attached by a rope, causing the system to move with an acceleration an in opposition to the force of gravity acting on one of the bodies. By dividing a body's mass (m) by the net force (F n e t) exerted on it, one can calculate the acceleration (a) of the body.

Please direct the bucket's acceleration in an upward direction.

The tension T supplied to the bucket is resisted by the weight mg acting downward, which causes the bucket to rise with an acceleration.

Applying the force balance we have as a result,

ma = T-mg

14a = 163-14 x 9.8

a = 1.84 m/s²

We can see that the acceleration is 1.84 m/s² times larger than the speed and since a has a positive sign, we can infer that the direction is upward.

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