Commons

f / Example 8.backward momentum, so the total momentum is still zero. Thekinetic energies of the gun and bullet are both positive numbers,however, and do not cancel. The total kinetic energy is allowedto increase, because both objects’ kinetic energies are destinedto be dissipated as heat — the gun’s “backward” kinetic energydoes not refrigerate the shooter’s shoulder!The wobbly earth example 7As the moon completes half a circle around the earth, its motionreverses direction. This does not involve any change in kineticenergy, because the moon doesn’t speed up or slow down, noris there any change in gravitational energy, because the moonstays at the same distance from the earth. 1 The reversed velocitydoes, however, imply a reversed momentum, so conservationof momentum tells us that the earth must also change its momentum.In fact, the earth wobbles in a little “orbit” about a pointbelow its surface on the line connecting it and the moon. The twobodies’ momenta always point in opposite directions and canceleach other out.The earth and moon get a divorce example 8Why can’t the moon suddenly decide to fly off one way and theearth the other way? It is not forbidden by conservation of momentum,because the moon’s newly acquired momentum in onedirection could be canceled out by the change in the momentumof the earth, supposing the earth headed the opposite directionat the appropriate, slower speed. The catastrophe is forbidden byconservation of energy, because both their kinetic energies wouldhave increased greatly.Momentum and kinetic energy of a glacier example 9A cubic-kilometer glacier would have a mass of about 10 12 kg —1 followed by 12 zeroes. If it moves at a speed of 0.00001 m/s,then its momentum would be 10, 000, 000 kg·m/s. This is the kindof heroic-scale result we expect, perhaps the equivalent of thespace shuttle taking off, or all the cars in LA driving in the samedirection at freeway speed. Its kinetic energy, however, is only 50joules, the equivalent of the calories contained in a poppy seedor the energy in a drop of gasoline too small to be seen withouta microscope. The surprisingly small kinetic energy is becausekinetic energy is proportional to the square of the velocity, and thesquare of a small number is an even smaller number.1 Actually these statements are both only approximately true. The moon’sorbit isn’t exactly a circle.48 Chapter 2 Conservation of Momentum