Simple Nature - Light and Matter

A car drives over a cliff.new frame of reference, a change from zero velocity to −2v, whichwould violate conservation of energy. In other words, the physicallypossible motion conserves energy in all frames of reference, but theunphysical motion only conserves energy in one special frame ofreference.For our second example, we consider a car driving off the edgeof a cliff (r). For simplicity, we assume that air friction is negligible,so only kinetic and gravitational energy are involved. Does the carfollow trajectory 1, familiar from Road Runner cartoons, trajectory2, a parabola, or 3, a diagonal line? All three could be consistentwith conservation of energy, in the ground’s frame of reference. Forinstance, the car would have constant gravitational energy alongthe initial horizontal segment of trajectory 1, so during that timeit would have to maintain constant kinetic energy as well. Only aparabola, however, is consistent with conservation of energy combinedwith Galilean relativity. Consider the frame of reference thatis moving horizontally at the same speed as that with which the carwent over the edge. In this frame of reference, the cliff slides outfrom under the initially motionless car. The car can’t just hoverfor a while, so trajectory 1 is out. Repeating the same math as inexample 8 on p. 83, we havex ∗ = 0 ,y ∗ = 1 2 gt2in this frame of reference, where the stars indicate coordinates measuredin the moving frame of reference. These coordinates are relatedto the ground-fixed coordinates (x, y) by the equationsx = x ∗ + vt and y = y ∗ ,where v is the velocity of one frame with respect to the other. Wetherefore havex = vt , y = 1 2 gt2 ,in our original frame of reference. Eliminating t, we can see thatthis has the form of a parabola:y =g2v 2 x2 .self-check AWhat would the car’s motion be like in the * frame of reference if itfollowed trajectory 3? ⊲ Answer, p. 92290 Chapter 2 Conservation of Energy