An interesting exhibit at Gettysburg is two lead balls that are stuck/ melted to

Question

An interesting exhibit at Gettysburg is two lead balls that are stuck/ melted together. During the battle of gettysburg, the two balls had a head on collision. The balls stopped and dropped to the ground- melted together.

For this problem assume the balls are idential and traveling at some speed in opposite directions.

During the collision, aall of their kenetic energy is converted into heat. Also assume that 40%of the mass of each ball is mealted. The initial temperature is 30 Deg C.

FIND:

The speed of the balls just before their collision. You can use the following constants for lead.

C=128J/kgk, Tmealt=328 deg c, Lf= 2.5x10^4 j/kg

Explanation / Answer

another way to approach this is to assume that both balls are heated upto 328C and then 40% of each melts...

the energy conservation equation wud then become

2 x 0.5Mv^2= 2 x MCdT + 2 x 0.4ML

we get V^2 = 2CdT + 0.8L = 96288

solving we get velocity V = 310.3 m/s

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