What is the tension in the string connecting a cork and a cube in water?

In summary, the problem involves a light string attached to a cork and a cube, with the cork submerged to 82% of its volume. The density of the cube is unknown and needs to be solved for. The density of an object is its mass divided by its volume, which can also be calculated using the forces acting on the cork, including the buoyant force, weight, and tension in the string.
  • #1
college boy19
5
0
One end of a light thin string is attached to the bottom of a 3.7 g, 42 cm3 cork. The other end is attached to a 58 g cube. The arrangement is placed in water and it is found that with 82% of the cork submerged the cube is held in equilibrium. What is the density of the cube in g/cm3?

I need help figuring out this problem.
 
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  • #2
Welcome to PF!

Hi college boy19! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
okay,
the density of an object is its mass divided by its volume:

D=m/v

so for the cube all i have in the equation is :
D= 58g/v

So i know that in order to get the density i need the volume of the cube.

this is where i am stuck.
 
  • #4
Hi college boy19! :smile:
college boy19 said:
So i know that in order to get the density i need the volume of the cube.

That's not the only way to get the density …

you can also work it out from the forces on the cork :wink:
 
  • #5
Well the forces acting on the cork are the buoyant force which is the the weight of the cork which is mg which is:

BF= 3.7*g
but gravity in SI units is 9.8kg/m^3 and I am using CGS units so gravity is 98g/cm^3
So the weight of the cork is

BF= 3.7(98)=362.6

the buoyant force = to the weight of the displaced fluid
 
  • #6
college boy19 said:
Well the forces acting on the cork are the buoyant force which is the the weight of the cork

No, the forces acting on the cork are the buoyant force, the weight, and the tension in the string.
 
  • #7
the buoyant force:
362.6
the weight:
mg=362.6
how do i figure out the tension in the string?

is it the buoyant force - the weight of the cube
 
  • #8
college boy19 said:
the buoyant force:
362.6
the weight:
mg=362.6

How can the buoyant force be equal to the weight?

How is buoyant force defined?
how do i figure out the tension in the string?

You have two equations for it …

one for the cork, and one for the mass …

that should be enough to solve the whole problem. :smile:
 

FAQ: What is the tension in the string connecting a cork and a cube in water?

What is the density of a cube?

The density of a cube is the amount of mass per unit volume of the cube. It is a measure of how tightly packed the particles are within the cube.

How is the density of a cube calculated?

The density of a cube can be calculated by dividing the mass of the cube by its volume. The formula for density is: density = mass / volume.

What is the unit of measurement for density?

The unit of measurement for density is typically grams per cubic centimeter (g/cm3) in the metric system or pounds per cubic inch (lb/in3) in the imperial system.

Does the density of a cube change with size?

No, the density of a cube remains constant regardless of its size. This means that a small cube and a large cube made of the same material will have the same density.

How does the density of a cube affect its buoyancy?

The density of a cube determines whether it will float or sink in a liquid. If the density of the cube is greater than the density of the liquid, it will sink. If the density of the cube is less than the density of the liquid, it will float.

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