A bowling ball weighing 71.2 N is attached to the ceiling by a 3.70 m rope. The ball is pulled to one side and released; it then swings back and forth like a pendulum. As the rope swings through its lowest point, the speed of the bowling ball is measured at 4.20 m/s. At this instant, what are (a) the acceleration of the bowling ball, in magnitude and direction, and (b) the tension in the rope?

a, 7.26kg

b, 36.59N

Explanation:

The question says it swings like a pendulum, as such, we would use the formula for circular acceleration.

a = v²/r

a = 4.2²/3.7

a = 17.64/3.7

a = 4.77m/s²

The acceleration of the ball is directed towards the centre because circular acceleration is usually directed towards the centre

To find tension, recall, F = ma

m = F/a

m = 71.2/9.81

m = 7.26kg

In solving for tension then, we use our acceleration to be (9.81 - 4.77) = 5.04m/s²

Tension = ma

Tension = 7.26 * 5.04

Tension = 36.5904

Hence the tension in the rope is 36.59N

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