## Mastering Physics Solutions: Lifting a Bucket

Lifting a Bucket

Part A = 365 N

Solution Below:

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

Part A

What is the tension in the rope?

The answer is about 60 N. Since the bucket is not accelerating, the only force acting on it is gravity (6 kg * 10 m/s^2 = 60 N)

60 N

Part B

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?

Since the bucket is accelerating upwards, the applied force is counteracting gravity. This means T = mg + F:

T = mg + F
T = 6 * 10 + (6 * 3)
T = 78 N

78 N

Part C

Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude 3 m/s2.

Since the bucket is accelerating downwards, the rope is not fixed and only a part of the gravitational force is creating tension. Just subtract the downward acceleration from g and multiply by the mass. This will give you about 42 N.

42 N

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