I don't now what dimesional formula this is and how to solve it?

ok i have a work sheet the first practice problem is:

Is the equation 8kg + 4kg = 12kg/s dimesionallyy corect

length legnth legnth

------- = ------- + -------x time2 2 it means squared

time time time

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  • 1 decade ago
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    Is the equation 8kg + 4kg = 12kg/s dimensionally correct

    Incorrect...the LHS of the equation has only mass dimension (kg)...the RHS has both mass and time (sec). Thus the dimensions are not equal between the LHS and the RHS of that = sign.

    length length leg nth

    ------- = ------- + -------x time2

    time time time

    Treat the dimensions like variables. On the LHS of =, we have L/T on the RHS, we have L/T + L/T * T^2 = L/T + LT. So, putting the two sides together, we have L/T = L/T + LT and 0 = LT, which is incorrect.

    Some things to note here.

    First use the ^, as in T^2, to denote an exponent.

    Second use symbols like L/T instead of words like length/time.

    Third, use the slash / to denote the divisor.

    Finally, when doing dimensional analysis, treat the dimensions as variables. That is, understand they add, subtract, multiply, and divide just like variables do.

    Here's the way I'd do your first problem.

    First, rewrite the equation with just the dimensions. Thus, M + M ~M/T and then M ~ M/2T. Thus 1 ~ 1/2T which is not true; therefore the dimensions are not equivalent. Do you see why? The mass dimensions canceled out leaving the time dimension left over. There should be no time dimension.

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  • gile
    Lv 7
    1 decade ago

    Both equations are dimensionally incorrect.

    In the first equation, although it's true that 8 + 4 = 12, the dimensions are not the same on both sides. On the left side it is Length, while on the right side it's Length/ Time

    Likewise, in the second equation, it's Length/Time on one side and LengthxTime on the other.

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