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Physics problem involving vectors and circles?
An object travels in a vertical circle of 1.88 m radius. When the object is traveling downward and is 24.5° from its lowest point, its total acceleration is a = (18.5i + 16.2j) m/s2. At this instant, determine the following. (Take the angle 24.5° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.)
a) magnitude of the radial acceleration
b) magnitude of the tangential acceleration
c) speed of the object
d) velocity of the object (Express your answer in vector form.)
1 Answer
- NCSLv 76 years agoFavorite Answer
The tangential and radial accelerations lie on perpendicular axes that are rotated 24.5º clockwise from the vertical/horizontal x/y axes.
a) 18.5 m/s² = a_r*sin24.5
a) a_r = [18.5sin24.5 + 16.2cos24.5] m/s² = 22.4 m/s²
b) a_t = [18.5cos24.5 - 16.2sin24.5] m/s² = 10.1 m/s²
c) speed v = √(a_r*r) = √(22.4m/s² * 1.88m) = 6.49 m/s²
d) velocity is perpendicular to acceleration, so is at an angle 24.5º below the +x axis:
V = 6.49m/s*cos24.5º i - 6.49m/s*sin24.5º j = 5.91m/s i - 2.69m/s j
barring computational error.
Hope this helps!
