3. Nick lifts 2 buckets of water up to the roof of his school. He plans to drop the water on his physics teacher. The 2 buckets are hung one above the other and pulled up the roof by a rope. The mass of the top bucket and its water is 9.00 kg, and the bottom bucket and its water has a mass of 6.00 kg. If the action reaction force between the buckets (the tension in the rope between the buckets) is 70.0 N, calculate: a) the acceleration [3]
b) the force applied by Jack to lift the 2 buckets up. [2]

a. The acceleration of the buckets is 1.8 m/s²

b) The force applied by Jack is 175 N

Explanation:

a. The given parameters are;

The mass of the top bucket and the water it contains, m₁ = 9.00 kg

The mass of the top bucket and the water it contains, m₂ = 6.00 kg

The tension in the rope between the buckets = 70.0 N

The tension in the rope between the buckets = The upward pulling force applied by Jack + The downward acting weight of the lower bucket

The upward pulling force applied by Nick on the lower bucket = F = m₂ × a

Where;

a = The acceleration given to the two buckets

∴ F = 6.00 kg × a

The downward acting weight of the lower bucket = m₂ × The acceleration due to gravity, g

∴ The downward acting weight of the lower bucket = 6.00 kg × 9.8 m/s² = 58.8 N

Which gives;

The tension in the rope between the buckets = 70.0 N = 6.00 kg. × a + 58.8 N

From which we have;

70.0 N = 6.00 kg. × a + 58.8 N

6.00 kg. × a = 70.0N - 58.8 N = 11.2 N

a = 11.2 N/(6.00 kg) = 1.8 m/s²

The acceleration, a = 1.8 m/s²

b) The force applied by Jack, F = The force moving the buckets up + The weights of the buck

∴ The force applied by Jack, F = Total mass × Acceleration + Weight of the two buckets

The force applied by Jack, F = (9.00 kg + 6.00 kg) × 1.8 m/s² + (9.00 kg + 6.00 kg) × 9.8 m/s². = 28 N + 147 N = 175 N.

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in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.