Conceptualize Conceptualize the situation using the figure and any experiences y

Question

Conceptualize Conceptualize the situation using the figure and any experiences you have had in driving over rises on a roadway.

Categorize Because the accelerating car is moving along a curved path, we categorize this problem as one involving a particle experiencing both tangential and radial acceleration. We recognize that it is a relatively simple substitution problem.

Analyze The radial acceleration is given by the following formula, with v = 8.00 m/s and r = 530 m. The radial acceleration vector is directed straight downward, and the tangential acceleration vector has magnitude 0.200 m/s2 and is horizontal.
Evaluate the radial acceleration:
ar = -
v2
r
= m/s2
Find the magnitude of :
a = ?ar2 + at2 = m/s2
Find the angle ? (see figure) between and the horizontal:
? = tan-1(ar / at) =

Explanation / Answer

ar = v2/r = 82/530 = 0.121 m/s2

a = 0.1212 + 0.22 = 0.234 m/s2
= tan-1(0.121 / 0.2) = 31.2°

ar = v2/r = 102/475 = 0.21 m/s2

Total acceleration a = 0.212 + 0.72 = 0.73 m/s2

= tan-1(0.21 / 0.7) = -16.7° west of north

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