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3 years ago

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It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinet

ic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature = 27.4 °C) for such an event to happen.

1 answer:

Amiraneli [1.4K]3 years ago

3 0

Answer:

354.72 m/s

Explanation:

$m$ = mass of lead bullet

$c$ = specific heat of lead = 128 J/(kg °C)

$L$ = Latent heat of fusion of lead = 24500 J/kg

$T_{i}$ = initial temperature = 27.4 °C

$T_{f}$ = final temperature = melting point of lead = 327.5 °C

$v$ = Speed of lead bullet

Using conservation of energy

Kinetic energy of bullet = Heat required for change of temperature + Heat of melting

$(0.5) m v^{2} = m c (T_{f} - T_{i}) + m L\\(0.5) v^{2} = c (T_{f} - T_{i}) + L\\(0.5) v^{2} = (128) (327.5 - 27.4) + 24500\\(0.5) v^{2} = 62912.8\\v = 354.72 ms^{-1}$

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<u>Friction Force</u>

When objects are in contact with other objects or rough surfaces, the friction forces appear when we try to move them with respect to each other. The friction forces always have a direction opposite to the intended motion, i.e. if the object is pushed to the right, the friction force is exerted to the left.

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Replacing in [1]

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From equation (1) above, we can say that the resistance (R) is inversely proportional to the square of the diameter of the wire. This implies that an increase in the diameter of the wire will result in a decrease of the resistance. Also, a decrease in the diameter of the wire will result in an increase in the resistance of the wire.

1. Since the diameter of the wire is increase, therefore, the resistance of the wire will decrease.

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