# (Solved): PLEASE ONLY ANSWER 15C AND 15D thumbs down if not answered (a) Explain the different reasoning be ...

(a) Explain the different reasoning behind the Galilean and the Lorentz transformation equations. [2] (b) Discuss the significance of the use of 4-vectors in Special Relativity, drawing comparison with 3-vectors where appropriate. Detailed mathematics is not necessary. [6] (c) Show that the 4-force of a particle can be expressed as $$\boldsymbol{F}=m_{0} \boldsymbol{A}$$. You may assume the expression for 4-acceleration: $\boldsymbol{A}=\gamma(u)\left(\gamma(u) \boldsymbol{a}+\frac{d \gamma(u)}{d t} \boldsymbol{u}, i c \frac{d \gamma(u)}{d t}\right)$ Under what conditions would this expression for $$\boldsymbol{F}$$ cease to be valid? [6] (d) Consider a particle of rest mass $$m_{0}$$ moving with 4-velocity $$\boldsymbol{U}$$ being subject to a 4-force $$\boldsymbol{F}$$. By considering the scalar product $$\boldsymbol{U}$$. $$\boldsymbol{F}$$ show that: $c^{2} \frac{d m}{d t}=\boldsymbol{u} \cdot \boldsymbol{f}+\frac{c^{2}}{\gamma(u)} \frac{d m_{0}}{d t}$ where $$\boldsymbol{u}$$ and $$\boldsymbol{f}$$ are the corresponding 3-D velocity and force respectively. [6]