A student says: "I can find s = ut + 1/2at² by dimensions alone." Explain why not, and give two…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A student says: "I can find by dimensions alone." Explain why not, and give two more limits of the method.
Need a reminder? The key ideaShow
If a quantity depends only on , and , write it as and match the powers of M, L and T on both sides. The pure number must come from theory or experiment.
The method finds a single product of powers; it is blind to pure numbers.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The sum. The method gives one product, . The formula is a sum of two terms, and , so it cannot come out.
Step 2. Pure numbers. It cannot find the , or a anywhere.
Step 3. More limits. It cannot give a relation with , or in it; it fails when more quantities are involved than there are base dimensions; and it cannot tell work from torque.
Answer: The formula is a sum; dimensions give one product, and miss pure numbers, functions and look-alike quantities.
Watch out. "Passes the dimension check" does not mean "derived by dimensions". passes, but it cannot be found this way.
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