A bullet of mass 5 gram is charged to 1 C. Through what potential difference it must be accelerated, so that it can acquire a speed of 100 m/s, starting from rest?
Question
A bullet of mass 5 gram is charged to 1 C. Through what potential difference it must be accelerated, so that it can acquire a speed of 100 m/s, starting from rest?
Solution
To solve this problem, we need to use the principle of conservation of energy. The kinetic energy gained by the bullet is equal to the electrical potential energy lost.
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First, convert the mass of the bullet into kilograms. 1 gram = 0.001 kg, so 5 grams = 0.005 kg.
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Calculate the kinetic energy (KE) the bullet needs to reach the desired speed using the formula KE = 1/2 * m * v^2, where m is the mass and v is the speed. Substituting the given values, we get KE = 1/2 * 0.005 kg * (100 m/s)^2 = 25 Joules.
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The electrical potential energy is given by the formula PE = q * V, where q is the charge and V is the potential difference. We know that the bullet loses this much energy when it is accelerated, so we set this equal to the kinetic energy and solve for V: 25 J = 1 C * V.
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Solving for V, we find that V = 25 J / 1 C = 25 Volts.
So, the bullet must be accelerated through a potential difference of 25 Volts to reach a speed of 100 m/s.
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