Two connected buckets over a pulley with bricks

Shah 72 · May 23, 2021

A bucket of mass 3kg rests on scaffolding at the top of a building. The scaffolding is 22.5m above the ground. The bucket is attached to a rope that passes over a smooth pulley. At the other end of the rope there is another bucket of mass 3kg, which initially rests on the ground. The bucket at the top of the building is filled with 6kg of bricks and is gently released. As this bucket descends the other bucket rises.
Find how long it will take the descending bucket to reach the ground.
I have no clue how to solve this.
Initially the acceleration is zero as both the buckets are at rest. R= 90N for the top bucket and T= 30N for the bottom bucket.

topsquark · May 23, 2021

What have you tried? Did you start by sketching out a Free Body Diagram?

-Dan

Shah 72 · May 24, 2021

topsquark said:

What have you tried? Did you start by sketching out a Free Body

Handwritten diagram of two 3 kg masses connected by a string over a pulley; one mass hangs against a wall labelled 2.5 m above the ground, the other rests on the ground, with tension T marked in the string.

Handwritten free-body diagram of a pulley system: a 3kg block on a horizontal surface tied by a string over a pulley to a hanging 3kg block, with tension T labelled, plus a separate diagram of a mass m with weight W, tension T and acceleration a, and the equations F = m x a and T = 9a.

Handwritten mechanics working, rotated sideways: a box labelled m2 with tension T up and weight W2 down and acceleration a down, then F = m x a, T - W2 = m2(-a), T - 30 = -3a, T = -3a + 30, 9a = -3a + 30, 12a = 30, a = 30/12, and s = ut + (1/2)at^2 with 2a.5 = 0 + (1/2) x 30/12 x t^2.

Shah 72 · May 24, 2021

topsquark said:

What have you tried? Did you start by sketching out a Free Body Diagram?

-Dan

I think I realized where I have done the mistake. I need to calculate the F= m×a of the 9kg bucket going down taking its acceleration as negative and the bucket of 3 kg coming up acceleration as positive. I get t= 3s
Is this the right way? My freeborn diagram is wrong for the bucket that's on the top

skeeter · May 24, 2021

Handwritten physics sketch of a pulley with a 9 kg block hanging on the left and a 3 kg block on a surface on the right, with tension T and weights 9g and 3g marked in blue; beside it, handwritten equations 9g - T = 9a, T - 3g = 3a, 6g = 12a, and a = g/2.

Shah 72 · May 24, 2021

skeeter said:

View attachment 11159

Thank you!

Two connected buckets over a pulley with bricks

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