A 6kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string was F = ma F = (6kg * 9.8 m/s2) * 0a F = 58.8 N Now its asking 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?

Initially, the bucket of water is being pulled straight up by a string at a constant speed, which means the tension is [tex]T = (6kg * 9.8 m/s_{2})=58.8N[/tex], the same magnitude of the weight but it is directed upward.

When the speed of the bucket begins to change, and it has an upward constant acceleration of magnitude [tex]3 m/s_{2}[/tex], that means a total force or better tension in the rope of [tex]T = (6kg * (9.8 m/s_{2}+3m/s_{2}))=6kg * (12.8 m/s_{2})=76.8N[/tex]

priyankatutor priyankatutor · Answer 2 · 2022-02-09T14:28:50+01:00

The tension on the rope is 76.8 N. The tension is the force developed on a string or rope when it is stretched.

What is tension?

The tension is the force developed on a string or rope when it is stretched. So, tension is defined as the total stretch force on the rope.

So the tension on the rope will be,

[tex]T = m(g +a)[/tex]

Where,

[tex]T[/tex] - tension

[tex]m[/tex] - mass = 6 kg

[tex]g[/tex] - gravitational acceleration = 9.8 m/s²

[tex]a[/tex] - acceleration = 3 m/s²

Put the values in the formula,

[tex]T = 6 (9.8 +3)\\\\T = 76.8 \rm \ N[/tex]

Therefore, the tension on the rope is 76.8 N.

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