Question

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?

Answer 1

Answer:

The tension in the rope is 262.88 N

Explanation:

Given:

Weight $W = 150$ N

Length of rope $r = 4.1$ m

Initial speed of ball $v = 5.5 \frac{m}{s}$

For finding the tension in the rope,

First find the mass of rod,

$mg = 150$                          ( $g = 9.8 \frac{m}{s^{2} }$ )

  $m = \frac{150}{9.8}$

  $m = 15.3$ kg

Tension in the rope is,

  $T = mg + \frac{mv^{2} }{r}$

  $T = 150 + \frac{15.3 \times (5.5)^{2} }{4.1}$

  $T = 262.88$ N

Therefore, the tension in the rope is 262.88 N