Chapter 13.4, Problem 88E

(a)

To determine

To prove : The equation $\frac{dp}{dv}=\frac{m_0}{{\left(1-\frac{v^2}{c^2}\right)}^{\frac{3}{2}}}$ if $p=mv$ where $m_0$ is the “ mass of object when it is in rest”, $v$ is the velocity of object and $c$ is the velocity of light and relation between them according to Einstein’s theory is $m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$.

(b)

To determine

To prove: The equation $W=\frac{m_0{c}^2}{\sqrt{1-\frac{v_1^2}{c^2}}}-\frac{m_0{c}^2}{\sqrt{1-\frac{v_0^2}{c^2}}}$ if an object of mass $m_0$ change its velocity from $v_0\text{ to }{v}_1$.

(c)

To determine

To prove: The total relativistic Energy E of the body at rest mass m is given by the equation $E=m{c}^2$.