- #1
opticaltempest
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Hello,
I am looking for some help on the following problem:
http://img387.imageshack.us/img387/5481/problemuk7.jpg
I have some questions on part (b)
Here is my solution for (a):
Conservation of linear momentum:
[tex]\Delta p = p_f - p_i = m_f v_f - m_i v_i [/tex]
Solving for mass:
[tex]E = mc^2 \Rightarrow m = \frac{E}{{c^2 }}[/tex]
Substituting mass into conservation of linear momentum:
[tex]
\Delta p = \frac{{E_f }}{{c^2 }} \cdot v_f - \frac{{E_i }}{{c^2 }} \cdot v_i
[/tex]
Replace final velocity and initial velocity with [tex]c[/tex] since both velocities are the speed of the photons which are constant speed of light:
[tex]\Delta p = \frac{{E_f }}{{c^2 }} \cdot c - \frac{{E_i }}{{c^2 }} \cdot c
[/tex]
Simplify:
[tex]\Delta p = \frac{{E_f }}{c} - \frac{{E_i }}{c}[/tex]
[tex]\Delta p = \frac{{\Delta E}}{c}[/tex]
I think I may have a solution for part (b):
Using the conservation of mechanical energy:
[tex]\Delta E_{internal} = \Delta K [/tex]
[tex]1500 = \frac{1}{2}mv^2 [/tex]
[tex]1500 = \frac{1}{2}\left( {1.5} \right)v^2 [/tex]
[tex]v = \sqrt {\frac{{1500}}{{\left( {0.5} \right)\left( {1.5} \right)}}}[/tex]
[tex]v = 44.7 \mbox{ m/s}[/tex]
Does that look like a valid solution for part (b)?
I am looking for some help on the following problem:
http://img387.imageshack.us/img387/5481/problemuk7.jpg
I have some questions on part (b)
Here is my solution for (a):
Conservation of linear momentum:
[tex]\Delta p = p_f - p_i = m_f v_f - m_i v_i [/tex]
Solving for mass:
[tex]E = mc^2 \Rightarrow m = \frac{E}{{c^2 }}[/tex]
Substituting mass into conservation of linear momentum:
[tex]
\Delta p = \frac{{E_f }}{{c^2 }} \cdot v_f - \frac{{E_i }}{{c^2 }} \cdot v_i
[/tex]
Replace final velocity and initial velocity with [tex]c[/tex] since both velocities are the speed of the photons which are constant speed of light:
[tex]\Delta p = \frac{{E_f }}{{c^2 }} \cdot c - \frac{{E_i }}{{c^2 }} \cdot c
[/tex]
Simplify:
[tex]\Delta p = \frac{{E_f }}{c} - \frac{{E_i }}{c}[/tex]
[tex]\Delta p = \frac{{\Delta E}}{c}[/tex]
I think I may have a solution for part (b):
Using the conservation of mechanical energy:
[tex]\Delta E_{internal} = \Delta K [/tex]
[tex]1500 = \frac{1}{2}mv^2 [/tex]
[tex]1500 = \frac{1}{2}\left( {1.5} \right)v^2 [/tex]
[tex]v = \sqrt {\frac{{1500}}{{\left( {0.5} \right)\left( {1.5} \right)}}}[/tex]
[tex]v = 44.7 \mbox{ m/s}[/tex]
Does that look like a valid solution for part (b)?
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