05. Hints and Suggestions
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Let’s look again at the shot-putter.
In the shot put, a large mass is thrown at an angle of 22oabove horizontal, from a position of 2 m above the ground, a horizontal distance of 25 m.
Imagine a videotape of the shot put event. Fast-forward over the frames showing the shot putter picking up the shot and stepping into the ring. Begin to watch the imaginary videotape frame-by-frame as the shot putter begins to push the shot off of her shoulder and forward. Stop the videotape on the frame when the shot first leaves the putter’s hand.
Why is it so important that we begin the analysis at this frame and explicitly disregard all the motion that has taken place before this frame? The reason is that in every frame preceding this frame, the shot put was in contact with the putter. Thus, the putter was exerting a force on the shot. Since no information is presented concerning this force, we have no way to determine the acceleration during these frames and hence no way to determine any other kinematic variables. Thus, we disregard all motion preceding the instant the shot leaves the putter’s hand because that portion of the motion is simply impossible to analyze with the information provided. Once the shot leaves her hand, the only force acting on the shot is the force of gravity, which greatly simplifies the analysis.
Continue playing the imaginary videotape forward. Begin playing the tape frame-by-frame as the shot approaches the ground. Stop the videotape the frame before the shot hits the ground. We will stop our analysis at this frame. Why? Because starting with the next frame, the shot is in contact with the ground. Once in contact with the ground, an additional, unknown magnitude force begins to act on the shot. Once an unknown magnitude force begins to act, the acceleration of the shot becomes unknown and we are stuck. Thus, we conveniently stop our analysis before things get too complicated!
Since our analysis stops the instant before contact, note that the shot is still moving at this instant. (If it wasn’t, how could it ever reach the ground?) Thus, resist the temptation to think that the velocity of the shot is zero at the end of analysis. The velocity of the shot is ultimately equal to zero (after it makes a big divot into the ground) but that happens long after it strikes the ground and hence long after our analysis is finished.