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The energy gained by an electron as it is accelerated by an electric field is equal to the work done by the electric field itself, and this is equal to the product between the charge of the electron and the potential difference across which the electron traveled:
(1)
where e is the electron charge, and
is the potential difference between the initial and the final point of the electron, and this is equal to
(2)
where E is the intensity of the electric field and d is the distance covered by the electron. If we substitute (2) into (1), we find a final expression for the energy gained by the electron
where e is the electron charge, and
where E is the intensity of the electric field and d is the distance covered by the electron. If we substitute (2) into (1), we find a final expression for the energy gained by the electron
The emerging velocity of the bullet is <u>71 m/s.</u>
The bullet of mass <em>m</em> moving with a velocity <em>u</em> has kinetic energy. When it pierces the block of wood, the block exerts a force of friction on the bullet. As the bullet passes through the block, work is done against the resistive forces exerted on the bullet by the block. This results in the reduction of the bullet's kinetic energy. The bullet has a speed <em>v</em> when it emerges from the block.
If the block exerts a resistive force <em>F</em> on the bullet and the thickness of the block is <em>x</em> then, the work done by the resistive force is given by,
This is equal to the change in the bullet's kinetic energy.
If the thickness of the block is reduced by one-half, the bullet emerges out with a velocity v<em>₁.</em>
Assuming the same resistive forces to act on the bullet,
Divide equation (2) by equation (1) and simplify for v<em>₁.</em>
Thus the speed of the bullet is 71 m/s