Menu div.question,div.steps {font-size: 16px; padding: 10px;line-height: 20px; margin: 20px;} div.question{border: 1px solid #ccc;} div#solution .button{font-size: 20px; margin: 20px; width: 200px; padding: 10px; text-align: center;} div.hint,div.answer,div.steps{display: none;} div.pre_next{font-size: 30px; width:90%; margin:auto;} div.pre_next a.nav_pre{float:left;} div.pre_next a.nav_next{float:right;} div.title div.notes{ font-family:sans-serif, Arial; font-size: 18px; } 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? Hint Answer (a) kg\cdotm/s (b)N•s Show Steps (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