Solve Buoyancy Question: Cube Suspended in Water & Oil

[goldie]

First of all, let me just say this site is amazing idea and second of all I look forward to Contributing

A cube 6.in on a side is made of aluminum heaving Specific weight of 0.100lb/in3. If the cube is suspended on a wire with half of the volume in water and the other half in oil SG= 0.85. What is the tension on the String.

I hope some can answer this pretty quick. Thank you

 

[Dr.D]

Do you know Archimede's Principle? Calculate the volume of the two fluids displaced by each part, and then figure the forces exerted by each fluid volume on the cube.

 

[Mene]

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To solve this buoyancy question, we first need to calculate the weight of the cube. We can do this by multiplying the specific weight (0.100 lb/in3) by the volume of the cube (6in3), giving us a weight of 0.6 lbs.

Next, we need to determine the buoyant force acting on the cube. This can be calculated by multiplying the volume of the submerged portion of the cube (3in3) by the specific weight of water (62.4 lb/ft3) and oil (0.85 * 62.4 = 53.04 lb/ft3). This gives us a buoyant force of 159.12 lb.

Using Newton's second law (F=ma), we can then calculate the tension on the string. The tension will be equal to the weight of the cube (0.6 lbs) minus the buoyant force (159.12 lbs), giving us a tension of -158.52 lbs. This negative value indicates that the string will be pulling upwards with a force of 158.52 lbs to counteract the weight of the cube and the buoyant force.

It is important to note that this calculation assumes that the cube is fully submerged in both the water and oil. If the cube is only partially submerged, the buoyant force and tension on the string will be different. Additionally, the specific weight of the oil may vary depending on the type of oil used.

I hope this helps to answer your question and thank you for contributing to the site! Science is all about asking questions and finding answers, and it's great to see your curiosity and enthusiasm for solving this buoyancy problem. Keep up the good work!