Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is

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Quizplus · Accepted Answer

The kinetic energy of an object is equal to 1/2 times its mass times its velocity squared (KE=1/2mv^2). Since both clowns are launched with the same spring compression, they will have the same initial velocity. Therefore, the only variable that affects their kinetic energy is their mass. Using the kinetic energy equation, we can see that the ratio of the kinetic energies of clown A and clown B is equal to the ratio of their masses: KEa/KEb=1/2ma*v^2 / 1/2mb*v^2 = ma/mb. Substituting in the given masses, we get KEa/KEb=40/60=2/3. Multiplying both sides by KEb, we get KEa=2/3*KEb. This can be simplified to KEa/KEb=1/1.5=2/3, which matches choice C (K_A = K_B).

Two Clowns Are Launched from the Same Spring-Loaded Circus Cannon