I need to find the Force necessary to give a proton andacceleration of 10^19 m/s
ID: 1735183 • Letter: I
Question
I need to find the Force necessary to give a proton andacceleration of 10^19 m/s^2. I was thinking about using theequation from the book which is the momentum (p) = mu. Where gamma () = 1/(1-u^2/c^2). u is thevelocity of the proton, in this case u=.1c and c is the speed oflight constant. m= the mass of the proton 1.6726 x 10^-27 kg. For the problem I am unsure as to how I would use theacceleration to get the force. With classical physics I woulduse F = ma, where m = mass of proton and a = acceleration desiredin this case. But we are dealing with modern physics, does itmake a difference? In the end how would I solve thisproblem? I need to find the Force necessary to give a proton andacceleration of 10^19 m/s^2. I was thinking about using theequation from the book which is the momentum (p) = mu. Where gamma () = 1/(1-u^2/c^2). u is thevelocity of the proton, in this case u=.1c and c is the speed oflight constant. m= the mass of the proton 1.6726 x 10^-27 kg. For the problem I am unsure as to how I would use theacceleration to get the force. With classical physics I woulduse F = ma, where m = mass of proton and a = acceleration desiredin this case. But we are dealing with modern physics, does itmake a difference? In the end how would I solve thisproblem?Explanation / Answer
p = mu or F =3ma We have: a = 1019 m/s2 m = 1.6726 × 1027 kg u = .1c you are right to then use = 1/[1-(u2/c2)] so = 1/[1-(0.012 )] = 1.00005 F = (1.00005)3 (1.67 x 10-27 kg)(1019 m/s2 ) = 1.67 x 10-8 N it does make a difference if you were to use classical physicsinstead. The instances in which it would not make a difference isif the values in the equation were not extremely small as in themass of a proton and extremely fast--velocities close to the speedof light.