Question

Use the work-energy theorem to find the force required to accelerate an electron (m =9.11 × 10−31 kg) from rest to a speed of 1.50 × 109 m/s in a distance of 1.25 m.

Answer 1

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Answer 2

The work energy theorem states that the work done on any object of mass m is numerically equal to change in its kinetic energy. Mathematically,

$W = {\frac{1}{2}mv_{final}^2 - \frac{1}{2}mv_{initial}^2 }$

here, $v_{final} = 1.5\times 10^{9} m/s\\v_{initial} = 0 m/s\\m = 9.1\times 10^{-31} kg$

The work done on an object can also be written as :\\

$W = force(F) \times displacement(s)$[\tex]

therefore force(F) on an object can be written as:

$F = \frac{W}{s} \\or$

$F = \frac{\frac{1}{2}mv_{final}^2 - \frac{1}{2}mv_{initial}^2 }{s}$

hence,

$F = \frac{1}{1.25}\times \frac{1}{2}\times 9.1\times 10^{-31}-31[(1.5\times 10^9)^2 - 0]$

$= 8.19\times 10^{-13} N$