Physics 40s scaling and proportions .

In summary, to support a steel sphere with 4 times the original volume, the diameter of the wire must be increased by the sixth root of 4. To support a steel sphere with 4 times the original diameter, the diameter of the wire must be increased by the square root of 4. The strength of the wire is proportional to the square of its diameter, while the volume (and weight) of the sphere is proportional to the cube of its diameter.
  • #1
mp3guy
2
0
physics 40s scaling and proportions ...please help

the physics of a wire supporting a sphere...

A wire of .2cm in diameter is just strong enough to support a steel sphere. What must the diameter of the wire be if the following changes are made to the sphere?


A. new sphere has 4x the original volume
B. new sphere has 4x the original diameter


for part A.
-determine the relationship between the volume and the strength
-determine the relationship between the strength and the linear dimension
-determine the actual diameter

for part B.
-determine the relationship between the diameter and the strength
-determine the actual linear dimension


any help would be very much appreciated. I'm not really sure how you would relate changes in the wire to changes in the sphere...

thanks, mp3guy :smile:
 
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  • #2
I would assume that the wire being "just strong enough" means that the material is at maximum stress (force per cross-sectional area). Thus, to support more weight, you will need a thicker wire to maintain the same F/A.

Your job is to figure out how the weight of the sphere changes in each case, and then figure out how the diameter of the wire must change to support it.
 
  • #3
what complicates things is they don't give you a lot of info...besides increasing the sphere's diameter and volume by 4x in separate instances, you have no numbers to go by...what formulas would i use to solve this problem, or how do i find out the volume and linear dimension of the wire?
 
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  • #4
You are given all the information you need. For example: If the sphere's volume gets multiplied by 4, what happens to its weight? If its diameter gets multiplied by 4, what happens to its volume?

How does the volume of a sphere depend on its radius (or diameter)? (How does the volume of any shape depend on its linear dimensions?)
 
  • #5
Generally speaking, the strength of a wire is proportional to the area of a cross section of the wire which is itself proportional to the square of the diameter of the wire.

The volume (and therefore the weight) of a sphere is proportional to the cube of the diameter.

If the diameter of a sphere is multiplies by 4 (but the density remains the same) its weight is multiplied by the cube root of 4 so the wire must have diameter square root of that: sixth root of 4.
 
  • #6
HallsofIvy said:
If the diameter of a sphere is multiplies by 4 (but the density remains the same) its weight is multiplied by the cube root of 4 so the wire must have diameter square root of that: sixth root of 4.
You might want to rephrase that answer, Halls! :smile:
 

FAQ: Physics 40s scaling and proportions .

What is scaling in physics?

Scaling in physics refers to the concept of proportionality between different physical quantities. It involves comparing the ratios of measurements for different objects or systems, rather than the absolute values. This allows for the generalization and prediction of physical phenomena on different scales.

How does scaling impact the study of physics?

Scaling plays a crucial role in understanding and predicting physical laws and phenomena. It allows scientists to study the behavior of systems on different scales, from the microscopic to the macroscopic, and make connections between them. Scaling also helps in the development of models and theories that can be applied to a wide range of systems.

What is the difference between scaling and proportions in physics?

Scaling and proportions are closely related concepts in physics, but they have distinct differences. Scaling involves comparing the ratios of different measurements, while proportions involve comparing the absolute values of the measurements. In other words, scaling focuses on the relationship between quantities, while proportions focus on the quantities themselves.

How is scaling used in real-world applications?

Scaling is used in various fields, including engineering, biology, and economics. In engineering, scaling is used to design and test structures, such as buildings and bridges, on smaller scales before building them on a larger scale. In biology, scaling is used to study the relationships between different organisms and their environments. In economics, scaling is used to understand the behavior of markets and predict trends.

What are some examples of scaling and proportions in physics?

One example of scaling is the study of fluid dynamics, where the behavior of fluids on a large scale can be predicted by studying the behavior of individual molecules. An example of proportions is the relationship between the mass and volume of an object, which determines its density. Another example is the relationship between the force applied to an object and its resulting acceleration, as described by Newton's second law of motion.

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