Density of Log: Find Area Exposed & Calculate kg/m3

In summary, the given problem involves a round wooden log with a diameter of 83 cm, floating with 72% of its radius out of the water. The question asks for the log's density, with the given unit being kg/m3. To solve this problem, we can use the fact that the density of water is 1000 kg/m^3 and think about buoyancy. By understanding that the whole weight of the log is equal to the weight of the water displaced by the submerged portion of the log, we can determine the volume of that portion. This can be done by finding the area of the exposed end of the log and subtracting the area of the isosceles triangle cut off. Other methods, such as
  • #1
dstarnes
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0

Homework Statement


A round wooden log with a diameter of 83 cm floats with 72% of its radius out of the water. What is the log's density?
answer unit is kg/m3

Homework Equations



density of water= 1000 kg/m^3


The Attempt at a Solution


I've tried to find the area that is exposed, but do not know where to go from there.
 
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  • #2
Think about it in terms of bouyancy (sp?). Anything that floats like a boat or a log, does so because the volume of the water displaced has a weight that is equal to the weight of the object. So the whole weight of the log is equal to the weight of the water displaced by the partial cylinder that is under water. Use the facts in the problem statement to tell you what that volume portion would be, and go from there...
 
  • #3
ok i kind of understand what you are saying, but wanted some clarification on something. All right how am i to determine what the volume of the submerged part of the log is.
 
  • #4
dstarnes said:
ok i kind of understand what you are saying, but wanted some clarification on something. All right how am i to determine what the volume of the submerged part of the log is.

One way to do this is to think of the exposed area of the end of the log (a segment of a circle) as a sector (pie slice) of a circle with an isosceles triangle cut off. You can figure out the angles of the triangle and find the area of a segment as a fraction of the area of a circle, then subtract the area of the triangle. Then again you could look up the area of a segment, or use calculus to compute it.
 

FAQ: Density of Log: Find Area Exposed & Calculate kg/m3

What is density and why is it important to calculate?

Density is the measure of how much mass is contained in a given volume of a substance. It is important to calculate because it can help identify and characterize different materials, such as the type of wood in a log, and is also used in various scientific and engineering applications.

How do you find the area exposed of a log?

To find the area exposed of a log, you will need to measure the length, width, and height of the log. Then, calculate the surface area using the formula: 2[(length x width) + (length x height) + (width x height)]. This will give you the total surface area of the log.

How do you calculate the density of a log?

To calculate the density of a log, you will need to measure the mass of the log in kilograms and the volume of the log in cubic meters. Then, divide the mass by the volume to get the density in kilograms per cubic meter (kg/m3). The density of a log can vary depending on the type of wood it is made of.

What are some factors that can affect the density of a log?

The density of a log can be affected by factors such as the type of wood, the moisture content, and the age of the tree. Different types of wood have different densities, and the amount of water in the log can also impact its density. As a tree ages, the density of its wood can also change.

How does the density of a log impact its strength?

The density of a log can have a direct impact on its strength. Generally, the denser the wood, the stronger it will be. This is because denser wood has a tighter and more compact structure, making it more resistant to bending and breaking. However, other factors such as the grain and growth patterns also play a role in a log's strength.

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