A ball swings in a vertical circle at the end of a rope 1.50 mlong attached to t

Question

A ball swings in a vertical circle at the end of a rope 1.50 mlong attached to the ceiling. When the rope is 36.9 degrees pastthe lowest point and is on its way up, its total acceleration isgiven by (-22.5 i + 20.2 j) m/s2. At thatinstant determine the magnitude of its radial accelation and thespeed and velocity of the ball. I am confused about where to even begin. I don't reallyunderstand what they are telling me in the problem. A ball swings in a vertical circle at the end of a rope 1.50 mlong attached to the ceiling. When the rope is 36.9 degrees pastthe lowest point and is on its way up, its total acceleration isgiven by (-22.5 i + 20.2 j) m/s2. At thatinstant determine the magnitude of its radial accelation and thespeed and velocity of the ball. I am confused about where to even begin. I don't reallyunderstand what they are telling me in the problem.

Explanation / Answer

The ball is evidently swinging like a pendulum a2 = 22.52 + 20.22 =914.3    a2 = at2 +ac2     since thetangential and centripetal accelerations are perpendicular m at = m g sin 36.9     sinceonly the gravitational force acts parallel to the tangent ac = (914.3 -5.882)   = 29.66m/s2   using at = g sin36.9        the centripetalacceleration ac = v2 / R v = (29.66 * 1.5) = 6.67 m/s   vx = v cos 53.1 = 4 m/s vy = v sin 53.1 = 5.33 m/s Since the ball is moving upwards vx andvy will be positive    

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