Newton's Law Help?

Question

A 6-kg bucket of water is being pulled straight up by a string. The upward acceleration of the bucket is constant, with magnitude of 3 m/s^2.

The tension in the rope is then?

Now assume the bucket is accelerating downward, with magnitude 3 m/s^2.

The tension in the rope is then?

I need some help with this problem. Newton's Laws have really confused me. Any help would be great. Thanks!

Answer 1

Please remember that the earth is always pulling with an acceleration of 9.81m/s^2.
To pull straight up 6-kg bucket of water, the force needs to provide upward acceleration of 3 m/s^2 as well as overcome the gravity. Thus the tension is: 6kg*(3 m/s^2 + 9.81m/s^2) = 77(N).
To let the bucket to have an acceleration of 3 m/s^2 downwards, the string should overcome part of the gravity of 9.81m/s^2. Thus the tension is: 6kg*(9.81m/s^2 - 3 m/s^2) = 41(N)