Imagine building a large pendulum by attaching one end of a 3.25-meter-long cable to the ceiling and the other end to a bowling ball that weighs 64.5 N. If you pull the ball to the side, it will swing back and forth in a circular arc. In one experiment you measure the speed of the swinging ball to be 4.25 m/s as it passes through its lowest point (when the cable is vertical). At that moment, find a. the magnitude and direction of the ball's acceleration b. the tension in the cable

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**Pendulum Dynamics: Calculating Acceleration and Tension**

Consider constructing a large pendulum using a 3.25-meter-long cable attached to the ceiling, with a bowling ball weighing 64.5 N at the other end. If you displace the ball horizontally and then release it, it will oscillate in a circular path. During an experiment, you measure the ball's velocity to be 4.25 m/s as it traverses the lowest point of its swing (when the cable is vertical). At this specific point, determine:

a. The magnitude and direction of the ball’s acceleration.

b. The tension in the cable.
Transcribed Image Text:**Pendulum Dynamics: Calculating Acceleration and Tension** Consider constructing a large pendulum using a 3.25-meter-long cable attached to the ceiling, with a bowling ball weighing 64.5 N at the other end. If you displace the ball horizontally and then release it, it will oscillate in a circular path. During an experiment, you measure the ball's velocity to be 4.25 m/s as it traverses the lowest point of its swing (when the cable is vertical). At this specific point, determine: a. The magnitude and direction of the ball’s acceleration. b. The tension in the cable.
Expert Solution
Step 1

Given :

Length of string, L=3.25 m

Weight of the ball, W=64.5 N

Speed of the swinging ball at the lowest position, v=4.25 m/s

Note:

1 N=1 kg·m/s2

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