In a TV picture tube, electrons are emitted from the cathode with negligible speed and attain a velocity of 5 10⁶ m/s after travelling one centimeter. Assuming straight line motion, determine the constant force acting on the electron. The mass of the electron is 9.1 10⁻³¹ kg .

Step-by-step solution

Given initial velocity u = 0 , final velocity v = 5 10^6 m/s , distance s = 1 cm = 10⁻² m , and mass m = 9.1 10⁻³¹ kg . Using the equation of motion v^2 = u^2 + 2as : a = v^2 - u^2 2s a = (5 10^6)^2 - 0 2 10⁻² a = 25 10¹² 2 10⁻² = 1.25 10¹⁵ m/s ^2 The constant force acting on the electron is given by Newton's second law, F = ma : F = (9.1 10⁻³¹) (1.25 10¹⁵) F = 11.375 10⁻¹⁶ N F 1.1 10⁻¹⁵ N