A toy car with two motions
This experiment reinforces the x and y directions convention, and the use of vector arrows. It also shows that a motion can have different components.
Apparatus and materials
For each student or student group
transparent plastic sheet
Board or other suitable surface marked with grid lines
Health & Safety and Technical notes
The plastic sheet should be thick enough to prevent crumpling as it moves.
For grid lines, a spacing of 5 centimetres is adequate. Depending on student ability, it may be better if you prepare these before the lesson. Some students may be uncertain about "x direction" and "y direction". Label them on the boards.
a On a sheet of paper, draw a grid that is a smaller version of the one under the plastic sheet. This is a 'map' of the grid.
b Put the plastic sheet over the grid lines.
c Push the car steadily across the sheet in the x direction.
d On your map, mark the start and finish positions of the car. Draw a straight line that joins the starting and finishing positions. Draw an arrowhead on the line, with its point at the finishing position.
e With the car stationary on the sheet, pull the sheet in the y direction at a constant speed. Mark the start and finish positions on the map.
f Now one person should move the car in the x direction across the plastic while another person drags the plastic sheet in the y direction. Drag it as smoothly as you can, and not too fast. Don't let the car wheels 'skid'.
g You should find that the car has ended up at a different place on the grid. That is because it has 'two motions'. It has the motion you give it by pushing it, and the motion it gets from the moving plastic sheet. Make a new 'map' of the grid. Mark the starting and finishing positions, and join them with a journey arrow as you did before.
h You tried to push the car in the x direction. Draw an arrow to show what the motion would have been like if the plastic sheet had stayed still.
i The sheet moved in the y direction. Draw an arrow, starting in the same place as the others, to show the journey of the plastic sheet.
j Repeat this, but change the velocity of the car and/or the plastic sheet. You'll need to make a new map grid for each journey. Draw three arrows again, one for the x-direction motion, one for the y-direction motion, and one for the combined motion.
k Decide what pattern the arrows make.
l You can try all sorts of different combinations of motion of the car and the sheet. To keep it simple to start with, try changing only the direction in which you push the car. Try pushing it in the opposite direction to its original journey (in the 'negative' x direction). Then try moving the car and the sheet in the same direction. Always follow the rule that the car must never skid.
1 This can be as open-ended as you like. You could limit investigation to perpendicular motions, and guide students to the idea that the combined motion is shown by the diagonal of the rectangle that the separate motions make. Or students could try both perpendicular motions and co-linear motions, for which the resultant motion is a simple sum.
2 They could try a wider range of orientations of motions, but it becomes more difficult to see that the resultant is shown by the diagonal of a parallelogram.
This experiment was safety-checked in March 2005