Report Sheet Centripetal Acceleration
Data:
Radius (cm) Speed (cm)
Δv (cm) 9.0 3.0 2.0
9.0 6.0 8.0
4.5 3.0 4.0
1.
Based on the Δv vectors from the three Cases, what appears to be the direction of the acceleration of the object with respect to the point of interest, which was vertically above the center of the circular path? (i.e.: up, down, to the right, to the left, etc.)
2.
Given that the point of interest was arbitrarily chosen, what appears to be the direction
in general
of this type of acceleration? (Hint: the answer is in the name of this activity.)
3.
Given the numerical value of the ratio Δv
2
/Δv
1
for Cases 1 and 2, what appears to be the mostly likely algebraic relationship between the acceleration and constant speed for an object traveling in a circular path?
4.
Given the numerical value of the ratio Δv
3
/Δv
1
for Cases 1 and 3, what appears to be the mostly likely algebraic relationship between the acceleration and radius of the circle for an object traveling in a circular path?
5.
Combine the last two responses into a single relationship for acceleration, speed and radius for an object traveling at a constant speed on a circular path.
(Note that this model only allows us to predict the functional relationship between acceleration, speed and radius. We cannot write an
equation
for centripetal acceleration, only a proportionality.
A proportionality becomes an equation with the addition of a proportionality constant. The value of the constant depends on the measured values of the variables under experimental conditions and the choice of units. However, if speed, radius and acceleration are measured in
consistent SI units, the proportionality constant for the centripetal acceleration is "1".)
