Answer:
[tex]a_c=2.0196\times 10^{13}\ m/s^2[/tex]
[tex]F=3.37273\times 10^{-14}\ N[/tex]
Explanation:
m = Mass of proton = [tex]1.67\times 10^{-27}\ kg[/tex]
v = Speed of proton = 0.5c = [tex]0.5\times 3\times 10^8=1.5\times 10^8\ m/s[/tex]
Circumference of the colider is 7 km
[tex]P=2\pi r\\\Rightarrow r=\frac{P}{2\pi}\\\Rightarrow r=\frac{7000}{2\pi}\ m[/tex]
[tex]a_c=\frac{v^2}{r}\\\Rightarrow a_c=\frac{\left(1.5\times 10^8\right)^2}{\frac{7000}{2\pi}}\\\Rightarrow a_c=2.0196\times 10^{13}\ m/s^2[/tex]
Centripetal acceleration is [tex]2.0196\times 10^{13}\ m/s^2[/tex]
[tex]F_c=ma_c\\\Rightarrow F_c=1.67\times 10^{-27}\times 2.0196\times 10^{13}\\\Rightarrow F=3.37273\times 10^{-14}\ N[/tex]
Force on protons is [tex]3.37273\times 10^{-14}\ N[/tex]
