Dimensions of Force, Pressure: F, p

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SUMMARY

The discussion focuses on determining the dimensions of force (F) and pressure (p) using fundamental physical quantities: length (L), time (T), and mass (M). Force is defined by the equation F=ma, leading to the dimensional formula F = M(L/T²). Pressure is derived from the equation p=F/A, resulting in the dimensional formula p = M(L/T²)/L², which simplifies to p = M/(L·T²). This analysis clarifies the relationship between these physical quantities and their respective dimensions.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Basic knowledge of dimensional analysis
  • Familiarity with the concept of area in physics
  • Knowledge of fundamental physical quantities: length (L), time (T), mass (M)
NEXT STEPS
  • Study dimensional analysis techniques in physics
  • Learn about the derivation of physical quantities from fundamental principles
  • Explore the relationship between force, mass, and acceleration in detail
  • Investigate the applications of pressure in fluid mechanics
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Students of physics, educators teaching mechanics, and professionals in engineering fields who require a solid understanding of force and pressure dimensions.

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From the following defining equations, determine the dimensions of the names physical quantities. Use L to represent the dimension length (distance), T to represent time and M to represent mass.

a) force, F: F=ma, (where m is mass and a is acceleration)
b) pressure, p: p=F/A, (where F is a force (see previous question) and A is an area)

-I can't even attempt to solve this question as I have no idea what the question is asking for.
 
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The question is asking you to write force and pressure all in terms of the units L, T, and M. So for example, velocity is L/T.
 
OK so..

a) would be.. F=M(deltaL/deltaT) ?
b) how can I define A using only L, M or T?
 
No. Think about what you have written for force. That is saying that force is equal to mass times velocity. That is not correct. For part b, an area is simply two dimensions of length.
 
I still don't think I understand because this does not seem correct but..

a) F=M*d(L/T)/dT ?
b) p=M*d(L/T)/dT/L^2 ?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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