Speed of proton as fraction of c

[sheepcountme]

Homework Statement

Find the speed (as a decimal fraction of c) and momentum of a proton that has a kinetic energy of 1000MeV. The proton mass is 1.673x10^-27kg, or 938 MeV/c².

Homework Equations

KE= (1/2)mv²
KE= $$\gamma$$mc²
p=mv
$$\gamma$$=1/(sqrt(1-(v²/c²)))

The Attempt at a Solution

I'm not too sure about the KE, it's supposed to be 0.875c but I can't get that value...
I've been solving for gamma and then solving for u, but I get outrageous values.

 

[vela]

Your formula for the kinetic energy is wrong. That's probably why you're getting non-sensical results.

 

[sheepcountme]

Really? It's what our book gives us :/ Mind telling me what I should be using?

 

[vela]

I doubt that's what your book says. It's more likely you're just confusing the total energy with the kinetic energy. The total energy of an object of rest mass m is given by $E=\gamma mc^2$. Note when the object isn't moving and therefore has no kinetic energy, you still have $\gamma=1$ and $E_0=mc^2$. This energy E₀ is called the rest energy; it's the energy an object has just because it has mass. The kinetic energy of an object is the amount of energy in excess of the rest energy. Since the total energy is equal to $E=\gamma mc^2$ and the rest energy is $E_0=mc^2$, the kinetic energy is equal to $K=E-E_0=(\gamma-1)mc^2$.

 

[rwisz]

I would like to clarify some of the equations and values in this problem. The first equation, KE= (1/2)mv2, should be KE= (1/2)mv^2. Additionally, the value of 1000 MeV given for the kinetic energy of the proton should be converted to Joules (J) using the conversion factor 1 MeV = 1.602 x 10^-13 J. This gives a kinetic energy of 1.602 x 10^-10 J.

Next, we can use the equation KE= \gammamc2 to solve for the speed of the proton. Rearranging the equation, we get:

v = c * sqrt(1 - (m0c^2/KE)^2)

Substituting the values given in the problem, we get:

v = (3.00 x 10^8 m/s) * sqrt(1 - (938 MeV/c^2 / 1.602 x 10^-10 J)^2)

Solving this equation, we get a speed of 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999