Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_12

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/12 A general expression is given by , where is a dimensionless constant, is mass, and are lengths, and is time. Determine both the SI and U.S. units of , being sure to use the base units in each system. Problem 1/12 (a) Determination of SI Units ● Calculation Process 1. Present Final Formula: The dimensional expression for is derived from the given equation: Since is dimensionless, . The dimensions of the other variables are: mass , lengths , and time . 2. Substitute Values: In the SI system, the base units for mass, length, and time are: Mass (): kilogram () Length (): meter () Time (): second () Substituting these base units into the dimensional formula: 3. Final Calculation: Note: This combination is equivalent to the Newton-meter () or the Joule (), but the question specifically requests base units. Q=kmbc/t 2 k mbctQ Q [Q]= [t] 2 [k][m][b][c] k[k]=1 [m]=M[b]=[c]=L[t]=T [Q]= = T 2 1⋅M⋅L⋅L T 2 ML 2 mkg b,cm ts Units of Q= (s) 2 (kg)⋅(m)⋅(m) Units of Q= s 2 kg⋅m 2 N⋅mJ ● Final Conclusion: The SI units for in base units are (b) Determination of U.S. Customary Units ● Calculation Process 1. Present Final Formula: We use the same dimensional formula derived previously: 2. Substitute Values: In the U.S. Customary system, the primary base units for mechanics are force, length, and time: Force: pound () Length (): foot () Time (): second ( or ) Since mass () is a derived quantity in this system (), its representation in base units i