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Unless otherwise stated, in the following
Chapter 3, Problem 10E(choose chapter or problem)
Problem 10E
Problem
Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.
An object of mass 2 kg is released from rest from a platform 30 m above the water and allowed to fall under the influence of gravity. After the object strikes the water, it begins to sink with gravity pulling down and a buoyancy force pushing up. Assume that the force of gravity is constant, no change in momentum occurs on impact with the water, the buoyancy force is 1/2 the weight (weight = mg), and the force due to air resistance or water resistance is proportional to the velocity, with proportionality constant b1 = 10 N-sec/m in the air and b2 = 100 N-sec/m in the water. Find the equation of motion of the object. What is the velocity of the object 1 min after it is released?
Questions & Answers
QUESTION:
Problem 10E
Problem
Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.
An object of mass 2 kg is released from rest from a platform 30 m above the water and allowed to fall under the influence of gravity. After the object strikes the water, it begins to sink with gravity pulling down and a buoyancy force pushing up. Assume that the force of gravity is constant, no change in momentum occurs on impact with the water, the buoyancy force is 1/2 the weight (weight = mg), and the force due to air resistance or water resistance is proportional to the velocity, with proportionality constant b1 = 10 N-sec/m in the air and b2 = 100 N-sec/m in the water. Find the equation of motion of the object. What is the velocity of the object 1 min after it is released?
ANSWER:
Solution
Step 1
In this problem, we have to find the equation of motion of the object and then find the velocity of object after 1 min release.