4. Kinetic energy `K` has dimensions `kg \cdot m^2//s^2`. It can be written in terms of the momentum `p` and mass `m` as `K=p^2/(2m)` (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is the newton N,where `1 N =1kg\cdotm//s^2` .What are the units of momentum `p` in terms of a newton and another fundamental SI unit?
(a) `kg\cdotm/s` (b)`N•s`
(a) `K=p^2/(2m)` `p=sqrt(K•2m)` In this equation `m` is mass and it's SI unit is `kg`. `p = sqrt((kg•m^2)/s^2 times kg) = sqrt((kg^2•m^2)/s^2)` ` = sqrt(((kg•m)/s)^2) = (kg•m)/s` (b) `p = (kg•m)/s = (kg•m)/s^2 •s ` Where `(kg•m)/s^2 = N` `p = N•s`