2007-10-15

energy misconception

Here's an energy example problem I discuss briefly every year, because it brings up a serious student misconception. I did it today in class, and it worked as usual, although about one fifth of the class got it right straight off the bat.

A block slides from rest down a long, slanted ramp that ends with a small, up-turned ski jump (I usually draw the end of the ski jump at about 45 degrees elevation above the horizontal). Air resistance and friction are negligible. After sliding down the ramp and leaving the jump, the block will fly on a parabolic trajectory. Will the peak of that parabolic trajectory come up above the vertical height of the starting point, exactly to the height of the starting point, very slightly below the height of the starting point, or well below the height of the starting point?

The students want to go with to or slightly below. The correct answer is well below, because the trajectory in gravity never brings the horizontal component of velocity to zero, and therefore never brings the kinetic energy to zero, or even close to zero. This leads to a nice discussion and an instructive comparison with the typical roller-coaster problems out there.

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