Pressure, Buoyant Force problem

Click For Summary
SUMMARY

The problem involves calculating the density of a solid cube floating in water, where 1/4 of the cube is above the water surface. The relevant equations include density (density = mass/volume), buoyant force (Fb = density of fluid × volume of fluid × g), and pressure (P = density × height × g). The correct density of the cube is determined to be 750 kg/m³, derived from the relationship between the volume of the cube submerged and the density of the fluid, which is 1000 kg/m³. The initial miscalculation stemmed from incorrect area multiplication and misunderstanding of percentage representation.

PREREQUISITES
  • Understanding of buoyancy principles and Archimedes' principle
  • Familiarity with basic physics equations related to density and force
  • Knowledge of pressure calculations in fluid mechanics
  • Ability to manipulate algebraic equations for solving density problems
NEXT STEPS
  • Study Archimedes' principle and its applications in fluid mechanics
  • Learn about the relationship between buoyant force and submerged volume
  • Explore density calculations in various states of matter
  • Practice solving similar buoyancy problems using different shapes and fluids
USEFUL FOR

Students studying physics, particularly those focusing on fluid mechanics, as well as educators looking for examples of buoyancy and density calculations.

ChunkymonkeyI
Messages
35
Reaction score
0

Homework Statement


A solid cube of unkown material is floating upright in water so that 1/4 of the cube is above the surface of the water. What is the density of the material?


Homework Equations


Density=m/v
F=mg
Fb=density of fluid times volume of the fluid times g
P=density times height times g

The Attempt at a Solution


Since the cube is floating upright in the water I think that means that the force of weight is equal to the buoyant force.
P=density times h times g
P=1000 kg/m^3 times 1/4 times 9.80 which equals 2450 Pa
Then I used F=PA
F=2450 Pa times 1/4 which equals 612.5 N
Then I used F=mg
m=F/g
m=612.5 N/9.80 m/s^2
m=62.5 kg
I don't know what 2 do from there and I think one of my step is wrong because I multiplied the area by 1/4 but I don't think that's right can someone please help me and explain 2 me how to solve this problem
 
Physics news on Phys.org
(Density of the object / density of the fluid) x 100 = Prencentage of object's volume in the fluid
 
But when I do that I get the following:
b/1000 kg/m^3 times 100=3/4
100b/1000=3/4
1b/10=3/4
b=7.5 and b is the density of the object but on my sheet it says the answer is 750 kg/m^3 and its almost like my answer but the decimal is moved over and idk y. Maybe my work was wrong or something can u explain ?
 
hmzone said:
(Density of the object / density of the fluid) x 100 = Prencentage of object's volume in the fluid

But when I do that I get the following:
b/1000 kg/m^3 times 100=3/4
100b/1000=3/4
1b/10=3/4
b=7.5 and b is the density of the object but on my sheet it says the answer is 750 kg/m^3 and its almost like my answer but the decimal is moved over and idk y. Maybe my work was wrong or something can u explain ?
 
3/4=0.75 is not the Precentage dude, it's 75%
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 23 ·
Replies
23
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
13
Views
1K