High School

A 14.0-kg bucket is lowered vertically by a rope with a tension of 163 N at a given instant. What is the acceleration of the bucket, and is it directed up or down?

Denote the acceleration in m/s\(^2\), where up is positive and down is negative.

Answer :

The acceleration of the bucket is 1.84m/s², and the direction of the acceleration is upward.

The mass of the bucket is m = 14.0 kg

The tension in the rope is T = 163N

Let a be the acceleration of the bucket.

The weight of the bucket is

W = mg

=(14.0 kg) x (9.80m/s²)

= 137.20 N

As the tension in the rope is greater than the weight, the bucket is accelerating upward.

Now, using Newton's second law,

ma = T - mg

a = 163N - 137.20N / 14.0 kg

= 1.84m/s²

Hence, the acceleration of the bucket is 1.84m/s², and the direction of the acceleration is upward.

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