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- Homework Statement
- I have a question which has two part described below:

Let the force P to be described by the surface area A between the ice and the buildings. The paramater for ice is comp. str. Y, which has the dimesion of stress. i) Proove the max. force per unit area P/A is independent of A. ii) Ice is a brittle material. That suggest an alternative model, that relevant materia parameter might not be comp stress Y but might instead be fracture toughness K(FL^-3/2). Show that in that case P/A is not independent of A and find how it depends on A?

- Relevant Equations
- i )pi(1) = P^X1 * A^Y1 * Y^Z1

I tried to use dimensional analysis, there is variable for part i) m= P,A and Y also parameter is used in analysis is n=3(M,L,T). So m-n=0 number of dimensionless analysis group. I am confused at this step however I did this calculation to reach solution:

i) P=MLT-2 (Ice Force) m-n=4-3=1(number of dimensionless group)

γ =ML-2T-2 (Specific Weight) A=L2 (Contact Surface Area)

pi(1) = P^X1 * A^Y1 * Y^Z1

pi(1) =( P/A*Y)

How it shows P/A is not dependent of A? I could skip some points in this question also I stuck at part ii. Thanks for help!

i) P=MLT-2 (Ice Force) m-n=4-3=1(number of dimensionless group)

γ =ML-2T-2 (Specific Weight) A=L2 (Contact Surface Area)

pi(1) = P^X1 * A^Y1 * Y^Z1

pi(1) =( P/A*Y)

How it shows P/A is not dependent of A? I could skip some points in this question also I stuck at part ii. Thanks for help!