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Chapter 1: Q22DQ (page 263)

When an object breaks into two pieces (explosion, radioactivedecay, recoil, etc.), the lighter fragment gets more kineticenergy than the heavier one. This is a consequence of momentum conservation, but can you also explain it by using Newton鈥檚 lawsof motion?

Short Answer

Expert verified

Yes, we can explain this situation using Newton鈥檚 law of motion.

Step by step solution

01

Newton’sSecond law of motion and third law of motion.

Newton鈥檚 second law of motion

When a force is acting on an object, the time rate of change of itsmomentumequals the force.

Newton鈥檚 third law of motion.

When two objects exert forces on each other, these forces have the same magnitude but have opposite directions.

02

Discussion.

According to Newton鈥檚 third law during the break, each piece exerts a force on the other, which is equal in magnitude and opposite in direction.

And according to Newton鈥檚 second law, this momentum will provide momentum to each piece after the break.

Since two forces are equal

Therefore,

F1=F2m1a1=m2a2

From the above, we can conclude that if the mass is less acceleration will be more. If acceleration is more change in velocity will be more hence lighter fragment will have more final velocity thus more kinetic energy.

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