Two speeding lead bullets, one of mass 14.0 g moving to the right at 305 m/s and

Question

Two speeding lead bullets, one of mass 14.0 g moving to the right at 305 m/s and one of mass 7.50 g moving to the left at 375 m/s, collide head-on, and all the material sticks together. Both bullets are originally at temperature 30.0 degree C. Assume the change in kinetic energy of the system appears entirely as increased internal energy. We would like to determine the temperature and phase of the bullets after the collision. (Lead has a specific heat of 128 J/(kg K), a melting point of 327.3 degree C, and a latent heat of fusion of 2.45 Times io4 J/kg.) (a) What analysis model is appropriate for the system of two bullets for the time interval from before to after the collision? From the model, what is the speed of the combined bullets after the collision? How much of the initial kinetic energy has transformed to internal energy in the system after the collision? Does all the lead melt due to the collision? (e) What is the temperature of the combined bullets after the collision? or ) What is the phase of the combined bullets after the collision?

Explanation / Answer

so

Q = m c dT + mliquid L

1.13E3 = (14.0E-3+7.5E-3)*128*(327.3-30) + m*2.45E4

m liquid = 0.0127 kg = 12.7 g

so m solid = 14+7.5-12.7= 8.8 g

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