Answer to Question #1845 in Mechanics | Relativity for ken

Question

A proton is moving at 425 m/s. (a) How much work must be done on it to stop it?(answer in joules) (A proton has a mass of 1.67×10−27 kg.) (b) Assume the net braking force acting on it has magnitude 8.01×10−16 N and is directed opposite to its initial velocity. Over what distance must the force be applied?(in meters) Watch your negative signs in this problem.

Answer 1

(a) While moving with a speed of 425 m/s proton has the following kinetic energy:
K = mv²/2 = 1.67×10^−27* 425²/2 = 1.51×10^−22 J
Required work is equal to this energy.

(b) S = A/F = 1.51×10^−22 / 8.01×10^−16 N = 0.189×10^−6 m.