Question

Lecture #6 textbook homework check. A&E Chapter 6 problems 66, 68 and 70 do not have answers at the back of the book, so I would like to swap answers.

Answer 1

A&E 6-66)\[E_{total} = K_{potential} + E_{kinetic} = mgh + mv^{2}/2\]\[\lambda = h/mv\]\[\nu = mv^{2}/h\]
a) double energy\[(2m)gh + (2m)v^{2}/2 = 2(mgh + mv^{2}/2) = 2E_{total}\]
b) half wavelength\[h/(2m)v = h/2mv = \lambda/2\]
c) if mass can change, double mass; if not then no change in mass, but velocity increases by a factor of the square root of 2\[2\nu = 2mv^{2}/h = (2m)v^{2}/h = m(\sqrt{2}v)^{2}/h\]
A&E 6-68)\[6800tons=6.17*10^{6}kg\]\[18\pm0.1knots=9.26\pm0.05m/s\]\[\lambda=h/mv=1.16*10^{-41}m\]
\[\Delta x\Delta(mv)\ge \hbar/2\]\[\Delta x\ge (\hbar/2)(1/\Delta(mv))\]\[\Delta x_{minimum}=(\hbar/2)(1/m\Delta v)=1.17*10^{-40}m\]

A&E 6-70)\[2800lbs=1270kg\]\[80mph\pm3\%=35.8m/s\pm3\%\]\[\lambda=h/mv=1.46*10^{-38}m\]\[\lambda=1.46*10^{-38}m \lt n*1.7*10^{-27}=n_pm_p+n_nm_n=d_{nucleus}\]
\[\Delta x\Delta(mv)\ge \hbar/2\]\[\Delta x\ge (\hbar/2)(1/\Delta(mv))\]\[\Delta x_{minimum}=(\hbar/2)(1/m\Delta v)=3.87*10^{-38}m\]\[\Delta x\ge 1.5*10^{-36}in\]