MOTION: GRAVITATIONAL ACCELERATION
1. Determine the angle of the inclined ramp by measuring the sides of the triangle
formed by the incline and the horizontal.
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Take the difference between heights h1 and h; , and use sinA = A-I_h to determine A. ‘g
(Angle A is likely to be under 5 degrees.) g in
A = lo. ’1 1 degrees Record A in the summary Table 4.7 & 4.8
2. Computing an estimate of the value of the acceleration due
to gravity near Earth’s surface
The acceleration down and parallel to the track is due to the acceleration of gravity.
We can replace g with the sum of two components that add up to the same value
and direction, namely g,. plus a component perpendicular to the track.
Formal geometry can show the two angles labeled A in *-_-_.%_Ehll
the diagram have the same value. To see that more ”““°-.::;‘g§,_ Q = Q ”+ Ell
qualitatively, run a movie in your head that begins with P‘5″-._*
the track horizontal and Q vertical and perpendicular to J.
it. At that moment g“ = 0. Imagine raising the right end i r -” A”9′° _ “’”‘~~~- a
of the track’ more and more: the magnitude of the -5- y The ye.;m’g”‘shows
component of 9 parallel to the track will grow larger and the rE_laIiWE Size and
larger. Taken to an extreme by raising the track into a I] ‘L ;’:2′::’e°’r;nF::n“:j’-Le In
vertical orientation, g,. will have the same value as g. As ff gm“-w._
the angle of the track relative to the horizontal increases, at;
the other angle labeled A matches that increase exactly.
Using the definition of sin A for this right triangle, namely sinA = calculate a value
of the magnitude of g for your track’s incline.
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