A-sol - Chapter A Problems Blinn College Physics 2425 Terry...

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Chapter A - Problems Blinn College - Physics 2425 - Terry Honan Problem A.1 Suppose that x is a length, t is a time and a is an acceleration. To get a general expression for x as a function of both t and a, we choose the general form: x = k a m t n where k is a dimensionless constant. For this expression to be dimensionally correct what must m and n be? Solution to A.1 Since x is a length, t is a time and a is an acceleration we get: @ x D = L , @ t D = T and @ a D = L T 2 . A dimensionless constant has dimen- sion 1, so @ k D = 1. Equating the dimensions of both sides of our general expression gives: @ x D = @ k D @ a D m @ t D n ï L 1 T 0 = 1 ÿ K L T 2 O m μ T n = L m μ T n - 2 m When we equate the powers of L and T we get two equations: 1 = m and 0 = n - 2 m which has the unique solution m = 1 and n = 2 . Problem A.2 Three fundamental constants G, c and have dimensions: [ G ] = L 3 M ÿ T 2 , [ c ] = L T and [ ] = M L 2 T . (a) What must m , n and p be to make L 0 a length, when L 0 = G m ÿ c n ÿ p . (b) , called "h bar", is a rescaled version of Plank's constant h ; it is usually also called Plank's constant. = h 2 p = 1.054 μ 10 - 34 J ÿ s Using this and the values of G and c given in the book evaluate L 0 . Comment: G is Newton's Gravitational constant , c is the speed of light which plays a central role in Relativity and is called Plank's constant , which appears in Quantum theory. L 0 is known as the
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A-sol - Chapter A Problems Blinn College Physics 2425 Terry...

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