M-K2: Independence of Horizontal and Vertical Motion
 
PIRA: 1D60.10 

Equipment: 4-wheel cart which ejects a ball vertically upward from a center post, the ball which fits over the post, a metal slug to activate the trigger on the cart, an incline down which the cart rolls. The incline and cart are in Set 9 Cabinet 3 Shelf 1. There are several drilled balls for this demonstration, some wood and some cork. Both work well, though the wood ball is probably superior.

Setup: Place the ball on the vertical post and push it down to compress the ejection spring and cock the trigger. Make sure the post is straight. Set the cart on the table at approximately the position where you would like the ejection to take place. While holding the cart steady with one hand, activate the trigger underneath the cart with a finger of the other hand. If the returning ball does not fall in the can surrounding the vertical post, move the cart to a neighboring spot on the table until you do find a place level enough for the ball to return to the can on the cart. This preliminary is a must!

Once you have found a suitable spot, before moving the cart, reset the ball for firing as before and carefully move the metal slug to a position under the cart so that the edge just touches the trigger and the slug is so centered under the cart that the wheels will clear it as the cart rolls past. Then, and not till then, carefully back the cart away and up the incline (if you intend to use it).

If all of this is done in the presence of the class the students will see for themselves that the ball is ejected vertically upward and not forward. It is best to test this all out before class, however, mainly to determine the proper launching point and thus the proper speed at which to launch the cart.

Demonstrations: "Set the cart in motion so that the trigger strikes the slug at the proper speed. The ball will rise and later fall back into the can (or near it) while the cart is still in motion. You may have to try this several times before the ball actually falls cleanly back into the can.

"Let students comment or ask questions. Some perceptive student may ask something like ‘What about friction?’ or ‘Doesn't the cart slow down?’ or ‘Why doesn't the ball get ahead because we know the cart must be slowing down?’ Or you may introduce the subject by remarking that previous students have asked such questions. Tell the students that friction does play an important part. The air friction on the ball varies as the square of the speed of the ball in this speed range, while the rolling friction on the cart is essentially constant. Thus the effects of friction on the ball's motion relative to the effects of friction on the cart are greater at high speeds and less at lower speeds. (Here, the time interval is the same for each trial.)

"Repeat the experiment for a very slow speed and for a very high speed compared to the original speed, and the results will be quite evident.

"From this demonstration students should gain a clearer understanding of the independence of motion along orthogonal directions and of the difference between fluid friction and solid rolling friction." — Percy Carr (1970)