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A heavy ball with a weight of 150 N is hung from the ceiling of a lecture hall on a 4.1-m-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.5 m/s as it passes through the lowest point. What is the tension in the rope at that point?

Respuesta :

Answer:

The tension in the rope is 262.88 N

Explanation:

Given:

Weight [tex]W = 150[/tex] N

Length of rope [tex]r = 4.1[/tex] m

Initial speed of ball [tex]v = 5.5 \frac{m}{s}[/tex]

For finding the tension in the rope,

First find the mass of rod,

[tex]mg = 150[/tex]                          ( [tex]g = 9.8 \frac{m}{s^{2} }[/tex] )

  [tex]m = \frac{150}{9.8}[/tex]

  [tex]m = 15.3[/tex] kg

Tension in the rope is,

  [tex]T = mg + \frac{mv^{2} }{r}[/tex]

  [tex]T = 150 + \frac{15.3 \times (5.5)^{2} }{4.1}[/tex]

  [tex]T = 262.88[/tex] N

Therefore, the tension in the rope is 262.88 N

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