M-K1: Addition of Displacement Vectors
 
PIRA: Unknown 

Equipment: Large (2 ft. by 5 ft.) and small (2 ft. by 3 ft.) sheets of wrapping paper, adhesive or sticky tape, black felt marking pen, toy spring-driven auto, chock for auto (500 g slotted weight). The auto is located in Set 9 Cabinet 3 Shelf 1.

Setup: Place the larger sheet of paper on the table and tape it down so it won't slide. Over it place the smaller sheet of paper near the taped end. Near one corner of the upper paper mark with the pen a large spot easily visible from the back of the room. Directly under this mark make a similar mark on the lower paper.

Demonstration: "Place the toy auto with its spring wound up so that its right rear wheel is over these marks. Aim the auto more or less across the paper, but do not destroy the generality of the experiment by aiming at right angles to the length of the paper. With one hand release the auto while with the other you drag the upper paper along over the lower paper. When the auto is near the side opposite the starting position, simultaneously stop the auto with one hand and cease dragging the paper with the other. Block further motion of the auto by placing in front of it a heavy mass (such as a 500 g slotted weight).

"With the pen make a large spot under the right rear wheel of the auto. Pick up the auto in such a way that its drive wheels cannot spin and set it to one side, making sure that it is securely blocked by the 500 g weight. Then make large easily seen spots on the lower paper directly under the two spots on the upper paper. Set the upper paper to one side. Draw a heavy line on the lower paper from the spot under the starting spot at the beginning (A) to the spot under the starting spot at the end (B). Similarly, draw a line from B to the spot under the finishing spot at the end (C). On the line AB draw the head of an arrow so that this line becomes a vector representing the motion of the car due to the acting of the hand dragging the upper paper. Similarly, convert the line BC into a vector representing the motion of the car due to the action of its drive mechanism. Then draw the vector AC to represent the totaldisplacement of the car due to both agencies acting simultaneously.

"Do not belabor the points or distract attention from the chief purpose by trying to quantify the results. For the same reason draw all lines freehand. The IDEA of vector representation of directed quantities (e.g., displacement) and their addition is what you are trying to convey. Quantification should be reserved in most cases for recitation, tutoring, or laboratory.

"This demonstration is very good for making clear the velocity vectors important in air (or ship) navigation since any displacement divided by the time associated with that displacement is the average velocity of the object for the time interval. Here, the auto plays the role of the aircraft, the upper paper the role of the air mass in which the vehicle flies, and the lower paper the role of the ground.

"CAUTION: Treat the auto as if it had to last for your grandchildren; it may have to. In particular, when wound up it should always be placed against an obstacle so that it cannot get away and fall off the table. It is also wise to run down the motor completely by braking with the hand carefully as soon as the experiment is over certainly before the students come down after lecture to handle things. (If the motor is run down rapidly to the end, the spring can come off the anchor pin, and a major operation is necessary to put it in operating condition again. It will certainly not be available for a lecture the next hour).

"Hint: If the auto does not run when it is wound, it may be that one of the wheels is touching the body. Twist that wheel gently and it should run." ¾ Percy Carr (1970)