Two objects, A and B, of identical volume are placed in a bucket of water. Object A floats with half of its volume submerged while object B sinks to the bottom of the bucket. Which of the following describes the buoyant forces on the two objects? A). The buoyant force on A is equal to the buoyant force on B. B) The buoyant force on A is one half the buoyant force on B. C) The buoyant force on A is one fourth the buoyant force on B. D) The buoyant force on A is twice the buoyant force on B. E) The buoyant force on A is four times the buoyant force on B.

A cube-shaped block A of side length a is hanging from a spring balance D, which reads, in units of mass, Mp. The block is submerged in liquid C, which has a total mass of me and is inside beaker B with mass mp. The beaker rests on an electronic scale E with a readout of ME. a) Draw force diagrams for block A and beaker B. b) What is the mass mд of block A in terms of the given variables? c) What is the density pc of liquid C? d) The block is now pulled out of the liquid. What are the new readings M and Mg on the balance and scale? e) Compare the readouts of the balance and scale before and after the block is pulled from the liquid for the values a = 0.1 m, mg = 1 kg, mc = 5 kg, MD = 3.5 kg, and MĘ = 7.5 kg. E D B 7.50 00

The gravitational force exerted on a solid object is 5.25 N as measured when the object is suspended from a spring scale as in Figure a. When the suspended object is submerged in water, the scale reads 3.80 N (Figure b). Find the density of the object. kg/m³ Scale b TA B Mg T₂

A scientist is calculating the density of an ore sample. The scien- tist measures that the ore sample weighs 22.4 N in air. When the sample is suspended by a thin light cord and totally immersed in water, the tension in the cord is 14.2 N. What is the density of the ore sample that the scientist calculates. You can assume that any buoyant force from air is negligible.

How do you find the magnitude of buoyant force on an object dropped into a fluid given both the fluid density and object density? How do you then use this information to determine what fraction of the object is submerged?

Archimedes’ Principle states that the upward or buoyant force on an object within a fluid is equal to the weight of the fluid that the object displaces. For a partially submerged object, you can obtain information about the relative densities of the floating object and the fluid by observing how much of the object is above and below the surface. You can also determine the size of a floating object if you know the amount that is above the surface and the relative densities. You can see the top of a floating iceberg (see figure). The density of ocean water is 1.03 × 103 kilograms per cubic meter, and that of ice is 0.92 × 103 kilograms per cubic meter. What percent of the total iceberg is below the surface?

Q1): The mattress of a water bed is 2 m long by 2 m wide and 30 cm deep. A) Find the weight of the water in the mattress. B) Find the pressure exerted by the water on the floor when the bed rests in its normal position. Assume that the entire lower surface of the bed makes contact with the floor. C) What if the water bed is replaced by a 300-lb ordinary bed that is supported by four legs? Each leg has a circular cross section of radius 2 cm. What pressure does this bed exert on the floor?

A block of wood, whose volume is V = 0.050 m3, is attached to the bottom of a lake by means of a rope and it is completely immersed in the water. The block has a density of 0.75 × 103kg/m3 (while water has a density of 1.0 × 103 kg/m3). a) Compute the buoyant force and the weight acting on the block.b) What is the tension in the rope?c) If we cut the rope, the block will start accelerating towards the surface. Calculate its acceleration.

The gravitational force exerted on a solid object is 5.50 N as measured when the object is suspended from a spring scale as in Figure a. When the suspended object is submerged in water, the scale reads 3.44 N (Figure b). Find the density of the object. kg/m3 Scale