Applying Kinetic Energy Formula

Applying Kinetic Energy Formula

Exercise. I push a book along a perfectly smooth table, from rest until it reaches a velocity of 0.2 m/s. If the book is 0.3 kg, how much work did I do? Answer. The work done only produces kinetic energy and no heat, since there is no friction. So work done = kinetic energy = mv²/2 = 0.3 x 0.2² /2 = 0.006 J.

Exercise. A ball hits the ground with velocity 2 m/s, and bounces with velocity 1 m/s. If the ball is 0.5 kg, how much heat is produced? Answer. The kinetic energy has decreased on rebound. The difference is converted to heat, since no electricity or light is produced. Initial kinetic energy is mv²/2 = 0.5 x 2² /2 = 1 J. Final kinetic energy is mv²/2 = 0.5 x 1² /2 = 0.25 J. So heat produced is 1 - 0.25 = 0.75 J.

Exercise. A bullet flying at a velocity of 100 m/s penetrates 0.5 m into a block of wood. If the bullet is 0.001 kg, find the resistance it experiences in the wood. Answer. The bullet does work as it moves through the wood. The force F it applies to the wood is equal in magnitude to the resistance, according to Newton's third law. The work it does must come from its kinetic energy. So Fd = mv²/2. Then the resistance is F = mv²/(2d) = 0.001 x 100² / (2 x0.5) = 10 N.

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