A particle of 1 kg moving at 200 m/s strikes a block of metal weighing 600 kg and comes to an immediate stop. What is the rise in the temperature of the block if the specific heat of the metal is...

A particle of 1 kg moving at 200 m/s strikes a block of metal weighing 600 kg and comes to an immediate stop. What is the rise in the temperature of the block if the specific heat of the metal is 0.9 J/g*K

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The kinetic energy of a particle of mass 1 kg moving at 200 m/s is (1/2)*1*200^2 J = 20 kJ

As the particle comes to an instant stop when it strikes the block of metal with a mass 600 kg, all the kinetic energy gets converted to heat that raises the temperature of the block. As the mass of the particle is very small compared to the mass of the block it can be ignored.

The specific heat of the metal that makes up the block is 0.9 J/g*K. This implies that 0.9 J is required to increase the temperature of 1 g of the metal by 1 K. If the increase in the temperature of the block is T, we get T*600*1000 = 20 kJ

=> T = 20/600 = 0.03 K

The temperature of the block increases by 0.03 K due to the impact.

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