Tutorial Exercis
An electron of mass 9.11 x 10-31 kg has an initial speed of 2.50 105 m/s. It travels in a straight line, and its speed increases to 6.70 105 m/s in a distance of 5.30 cm. Assume its acceleration is constant. (a) Determine the magnitude of the force exerted on the electron
(b) Compare this force with the weight of the electron, which we ignored.
Part 1 of 4 - Conceptualize Visualize the electron as part of a beam in a vacuum tube, speeding up in response to an electric force. Only a very small force is required to accelerate an electron because of its small mass, and if this force is much greater than the weight of the electron then the gravitational force can be neglected.
Part 2 of 4 - Categorize
Since this is a linear acceleration problem, we can use Newton's second law to find the force as long as the electron does not approach relativistic speeds, that is, much less than 3 x 103 m/s. We know the initial and final velocities, and the distance involved. From these given quantities, we can find the acceleration in order to determine the force
(a) From 'y = ma and v,2 = v,2 + 2ax, we can solve for the acceleration and then find the force using the following.
v,2 - v,2 2x
Substituting to eliminate a, we have
m (v,2- v2) DF-- 2x,
Substituting the given values into the equation above, gives us the following. ]x 10-31 kg)[( x105m/s)2-( ( m) X1018 N
] x 105m/s)]
