## anonymous one year ago Determine if the equation given is dimensionally correct: $$\sf F=m(v^2)/(d^2)$$

1. anonymous

@dan815

2. anonymous

@Abhisar

3. Abhisar

Ok, so first of all you know what is the dimension of force right?

4. anonymous

Not really. This is my pre-physics summer work.

5. anonymous

Newtons?

6. anonymous

ML/T^2

7. Abhisar

Yes, dimension of force = $$\sf M^1L^1T-2$$ Do you understand how?

8. anonymous

F=ma, and acceleration=L/T^2

9. Abhisar

$$\huge \checkmark$$

10. Abhisar

So, in order to determine if the given equation is dimensionally correct we just need to make sure that same dimension occurs on both hand sides of the equation. So in RHS of equation the dimension should also be $$\sf M^1L^1T^{-2}$$

11. anonymous

Ok.

12. Abhisar

RHS = $$\sf \Large \frac{mv^2}{d^2}= \frac{mass \times (metre^2)}{second^2\times distance^2}$$ Agree?

13. anonymous

what? Okay, I have: $\frac{ mv^2 }{ d^2 }$ would equal $\frac{ M(L/T^2) }{ L^2 }$

14. Abhisar

$$\sf V=L/T \\ \Rightarrow V^2 = (L/T)^2=L^2/T^2$$

15. Abhisar

So, that would give you for RHS $\frac{ M(L^2/T^2) }{ L^2 }$ = $$\sf M/T^2$$

16. anonymous

yeah sorry i meant $\frac{ M \frac{ L^2 }{ T^2 } }{ L^2 }$

17. Abhisar

Yup, what can you say now, Is LHS = RHS?

18. anonymous

Yes? They've got the same letters...

19. Abhisar

LHS=Force= $$\sf M^1L^1T^{-2}$$ RHS=$$\huge \frac{ M(L^2/T^2) }{ L^2 }$$ = $$\sf M/T^2$$ Are they both equal?

20. anonymous

No, there's no L in the RHS. If there was, would they be equal?

21. Abhisar

Yes.

22. Abhisar

But since, RHS$$\neq$$LHS, the equation is dimensionally incorrect but if somehow they both were equal then the equation would have been dimensionally correct.

23. anonymous

so the letters just have to be there or does the division, etc. matter as well?

24. Abhisar

Division matters, treat them like algebraic variables.

25. anonymous

thank you!

26. Abhisar

Do you want me to give you some examples for practice?

27. anonymous

I have a few more to do in the packet. Hopefully I'll get it before class tomorrow. I think I understand better now. Thanks again

28. Abhisar

You're most welcome c:

29. anonymous

@Abhisar Would L=2.5L ?