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Re: The sign of g



From: Tina Fanetti <FanettT@QUEST.WITCC.CC.IA.US>

How do I explain to a student that when we choose up (+y) to be increasing, we say that the sign of g is negative, regardless of whether the ball is going up or going down.

Hi Tina.
A gemoetric approach is best here. First of all, "g" has no sign really because it's the magnitude of a vector quantity. It's inherently a positive but I don't even explain it as such. It's just a number that represents the magnitude of the gravitational acceleration near Earth's surface.

Here's the geometry. Use an arrow to represent the ball's velocity. Use a different style (or color) arrow to represent the gravitational acceleration. Acceleration includes a change in velocity. If *velocity* and *change in velocity (i.e. acceleration)* point in the same direction, the magnitude of the ball's velocity will increase and the velocity will be in that same direction. If *velocity* and *change in velocity (i.e. acceleration)* oppose each other, the magnitude of the ball's velocity will decrease even though the ball's velocity (vector) retains its original direction. Of course, if the acceleration acts for a sufficiently long duration, the velocity vector will indeed flip direction, but there's no need to call this direction "negative".

Here's a neat activity that reinforces this. Give each pair of students a little rubber ball. Have them roll it across their table (our students here sit two per table) at a slow, but constant speed (neglect friction). Have them draw an arrow that represents the ball's velocity vector. Now, as the ball rolls, have them give it a *nudge* with their fingertip in the direction of the ball's motion. Draw the (different!) arrow that represents the nudge. Have them compare the direction of the two arrows and lead them to realize that the ball's speed increased.

Repeat the activity, but this time direct the nudge so that it's opposite the ball's motion. Again, have them draw the appropriate arrows. If the nudge is gentle enough, they will see the ball slow down and even come to rest. The magnitude of the ball's velocity decreases due to the geometric nature of the *nudge* and the initial *velocity* vectors. If you use a bowling ball or a shotput, you'll be able to more easily demonstrate that the (bowling) ball's velocity changes direction as the nudge is applied so as to oppose the ball's initial velocity.

The geometric nature of velocity and acceleration vectors doesn't need predefined + or - directions.


Cheers,
Joe Heafner - Instructional Astronomy and Physics
Home Page http://users.vnet.net/heafnerj/index.html
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