A firearms company is testing a new model of rifle by firing a 7.50-g lead bullet into a block of wood having a mass of 17.5 kg. The bullet embeds into the block and the collision generates heat. As a consequence, the temperature rises by 0.040°C, as measured with a high-precision thermometer. Assuming that all the kinetic energy of the bullet goes into heating the system, what is the bullet's speed when it enters the block? The initial temperatures of bullet and wooden block can be considered identical and the specific heats of lead and wood are cPb = 130 J / (kg ⋅ C°) and c wood = 1700 J / (kg ⋅ C°), respectively.

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Physics

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4 August, 01:37

A firearms company is testing a new model of rifle by firing a 7.50-g lead bullet into a block of wood having a mass of 17.5 kg. The bullet embeds into the block and the collision generates heat. As a consequence, the temperature rises by 0.040°C, as measured with a high-precision thermometer. Assuming that all the kinetic energy of the bullet goes into heating the system, what is the bullet's speed when it enters the block? The initial temperatures of bullet and wooden block can be considered identical and the specific heats of lead and wood are cPb = 130 J / (kg ⋅ C°) and c wood = 1700 J / (kg ⋅ C°), respectively.

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Jaliyah · Answer 1

Let the bullets speed be V.

Kinetic energy = 1/2 mV² where m is mass of bullet

This energy is converted into heat Q which raises the temperature of target by Δ T.

Q = mc Δ T, m is mass, c is specific heat and Δ T is rise in temperature.

heat absobed by bullet

=.0075 x 130 x. 040

=.039 J

heat absorbed by block of wood

= 17.5 x 1700 x. 04

= 1190 J

Total heat absorbed

= 1190.039 J

So kinetic energy = heat absobed

= 1/2 x. 0075 x V² = 1190.039

V² = 317343.73

V = 563.33 m / s