A 0.71 kg spike is hammered into a railroad tie. The initial speed of the spike is equal to 3.8 m/s. If the tie and spike together absorb 38.2 percent of the spike’s initial kinetic energy as internal energy, calculate the increase in internal energy of the tie and spike. Answer in units of J.

1.96 J

Explanation:

From the law of conservation of energy

ΔU + ΔK = 0  where ΔU = internal energy change and ΔK = kinetic energy change. We neglect potential energy change since we are not given any information about it.

ΔU = -ΔK

ΔK = K₂ - K₁ where  K₁ = initial kinetic energy and K₂ = final kinetic energy = 0 where  ΔU = 0.382K₁

     = 0.382mv²/2  where m = mass of spike = 0.71 kg and v = initial speed of spike = 3.8 m/s

     = 0.382 × 0.71 kg × (3.8 m/s)²/2

     = 1.96 J

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