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A rock with mass m = 3.00 kg is suspended from the roof of
Chapter 12, Problem 96CP(choose chapter or problem)
Problem 96CP
A rock with mass m = 3.00 kg is suspended from the roof of an elevator by a light cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator, but the rock doesn’t touch the bottom or sides of the bucket. (a) When the elevator is at rest, the tension in the cord is 21.0 N. Calculate the volume of the rock. (b) Derive an expression for the tension in the cord when the elevator is accelerating upward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2 upward. (c) Derive an expression for the tension in the cord when the elevator is accelerating downward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2 downward. (d) What is the tension when the elevator is in free fall with a downward acceleration equal to g?
Questions & Answers
QUESTION:
Problem 96CP
A rock with mass m = 3.00 kg is suspended from the roof of an elevator by a light cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator, but the rock doesn’t touch the bottom or sides of the bucket. (a) When the elevator is at rest, the tension in the cord is 21.0 N. Calculate the volume of the rock. (b) Derive an expression for the tension in the cord when the elevator is accelerating upward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2 upward. (c) Derive an expression for the tension in the cord when the elevator is accelerating downward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2 downward. (d) What is the tension when the elevator is in free fall with a downward acceleration equal to g?
ANSWER:Solution 96CP
Step 1:
A) The rock has three forces that affect the rock’s acceleration. When the rock is accelerating upward, the tension and the buoyant force are the upward forces. The rock’s weight is the downward force.
W =3.00kg9.8m/s=29.4
T=21N
Buoyant force = W-T
=29.4 - 21= 8.4
Buoyant force= density g
volume of displaced water.
Density=1000 kg/m3,g=9.8 m/s2
The volume of displaced water is equal to rock’s volume.
This is approximately 0.0008571.