PHYSICS HIGH SCHOOL

A hollow plastic sphere is held below the surface of a fresh-water lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.650 cubic meters and the tension in the cord is 900 N. a) Calculate the buoyant force exerted by the water on the sphere. b) what is the mass of the sphere? c) the cord breaks and the sphere rises to the surface. When the sphere comes to rest, what fraction of its volume will be submerged?

Answers

Answer 1

Answer:

Answer: a) B = 6811N

b) m = 603.2kg

c) 86.8%

Explanation: Buoyant force is a force a fluid exerts on a submerged object.

It can be calculated as:

$B=\rho_(fluid).V_(obj).g$

where:

$\rho_(fluid)$ is density of the fluid the object is in;

$V_(obj)$ is volume of the object;

g is acceleration due to gravity, is constant and equals 9.8m/s²

a) For the hollow plastic sphere, density of water is 1000kg/m³:

$B=10^(3).0.695.9.8$

B = 6811N

b) Anchored to the bottom, the forces acting on the sphere are Buoyant, Tension and Force due to gravity:

B = T + $F_(g)$

B = T + mg

mg = B - T

$m=(B - T)/(g)$

Calculating:

$m=(6811 - 900)/(9.8)$

m = 603.2kg

c) When the shpere comes to rest on the surface of the water, there are only buoyantandgravity acting on it:

B = m.g

$\rho_(w).V_(sub).g=m.g$

$V_(sub)=(m)/(\rho_(w))$

$V_(sub)=(603.2)/(1000)$

$V_(sub)$ = 0.6032m³

Fraction of the submerged volume is:

$(V_(sub))/(V_(obj))$ = $(0.6932)/(0.695)$ = 0.868

Answer 2

Answer:

Final answer:

We use the principles of buoyancy and Archimedes' principle to calculate the buoyant force, the mass of the sphere, and the fraction of volume submerged when the cord breaks. The buoyant force equals the weight of water displaced by the sphere, we will find this by calculating the difference between the weight of the sphere in air and its weight when submerged in water. The sphere's mass can be found using its volume and the density of plastic, whilst the fraction of volume volume submerged when the cord breaks will be such that the weight of water displaced equals the weight of the sphere.

Explanation:

To answer these questions, we will apply the principles of buoyancy and Archimedes' principle. Archimedes' principle states that the buoyant force on an object is equal to the weight of fluid displaced by the object. Buoyant force is hence the difference between the weight of the object in air and its weight when submerged in water.

(a) Calculating the buoyant force:

The total force acting on the sphere when it is submerged is the sum of the weight of the sphere (i.e., mass of sphere times the gravitational acceleration) and the tension in the cord. Since the sphere is at equilibrium, this total force equals the buoyant force exerted by the water. We can calculate the weight of the sphere in water as the weight of the sphere (mass x gravity) less the tension in the cord (900N).

(b) Calculating the mass of the sphere:

We can calculate the mass of the sphere by using the volume of the sphere and its density (which is the mass divided by the volume). Since the sphere is of plastic, we can look up or be provided the density of plastic to plug in here.

(c) Determining the fraction of volume submerged when the cord breaks:

When the cord breaks, the sphere will rise until the buoyant force and the weight of the sphere balance out. This happens when the amount of water displaced weighs the same as the sphere. The fraction of the sphere's volume that needs to be submerged to displace an amount of water with the same weight as the sphere will give the fraction of the spherical volume submerged.

Learn more about Buoyant Force here:

brainly.com/question/20165763

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Answers

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Answers

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