Physics
posted by Sonya .
A car is traveling over the top of a hill, which we will model to be a piece of a circular arc of radius R. For each case below, draw careful toscale motion maps and use them to construct the velocity vectors at the following three points: the top of the hill; equal time intervals on either side of the hill. Use the latter two velocity vectors to construct the average acceleration vector a at the top of the hill. Evaluate and comment on the direction and relative magnitude of a for the following cases:
(a) The car is moving at constant speed v over a hill of radius R.
(b) The car is moving at constant speed 2v. Quantitatively, how does the magnitude a change compared to that in part (a)?
(c)The car is moving at constant speed v over a hill of radius R/2. Quantitatively, how does a now compare to that obtained in part (a)?
(d)Brownie points:From your results of parts (a)(c), obtain an expression for the magnitude of the acceleration for the case of uniform circular motion (constant speed). Hint: what variables could the acceleration depend on? There is only one possible combination of those variables that will give you the right units!And your graphical constructions in parts (a)(c) should confirm the functional dependences.
(e)The car speeds up as it goes over the top of the hill; the car slows down as it goes over the top of the hill. Discuss your results for this nonuniform circular motion in the context of the “superposition principle:” the idea that a seemingly complex motion (accelerating over a hill) can be broken down into the superposition (addition) of two simpler motions – perhaps better described here as a decomposition.
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