Question

Find the gamma constant for objects traveling close to the speed of light. Here we are experimenting several speeds of light constants (even though the true speed of light is known). Below are the velocities of the objects and the speed of light constants used. V=[ 2.9, 2.6, 1.7, 2.1, 3, 1.01, 2.36] * 10^8 m/s C=[3, 3.1, 2.9] *10^8 m/s 1 v= 1- c2

How do I solve using Matlab?

Answer 1

• In this program we have to find the gamma value for each combination of V and C.

Program plan:

• define two vectors v and c with given values.
• loop through each index of v and c, calculate gamma and add it a vector.
• Tabulate the values of v, c and gamma

program

v = [2.9,2.6,1.7,2.1,3,1.01,2.36]*1e8;

c = [3,3.1,2.9]*1e8;

g = @(v,c) 1/(1-(v/c)^2)^0.5;

gamma = [];

for i = 1:length(v)

for j = 1:length(c)

gamma = [gamma; v(i) c(j) g(v(i),c(j))];

end

end

T = table(gamma(:,1),gamma(:,2),gamma(:,3));

T.Properties.VariableNames = {'v','c','gamma'};

disp(T)

output:

V c gamma 2.9e+08 2.9e+08 2.9+08 2.6e+08 2.6e+08 2.6e+08 1.7e+08 1.7e+08 1.7e+08 2. le+08 2. le+08 2. le+08 3e+08 3e+08 Se+08 1.01e+08 1.01e+08 1.0le+08 2.36e+08 2.36e+08 2.36e+08 3e+08 3.le+08 2.9+08 3e+08 3.le+08 2.9+08 Be+08 3.le+08 2.9+08 3e+08 3.le+08 2.9e+08 3e+08 3. le+08 2.9e+08 3e+08 3.le+08 2.9+08 Be+08 3. le+08 2.9e+08 3.9057+0i 2.8299+01 Inf+01 2.0045+01 1.8363+0i 2.2576+0i 1.2137+01 1.1959+0i 1.2343+0i 1.4003+0i 1.3594+0i 1.45+0i Inf+0i 3.9691+01 0-3.7755i 1.062+0i 1.0577+0i 1.0608+0i 1.6198+0i 1.5422+0i 1.7207+0i