Question

A simple pendulum is constructed by attaching a 0.540 kg ball to a 0.830 m long cord of negligible mass. If air resistance is negligible and the pendulum is swinging such that its maximum angular displacement is 30.0° determine the following.

(a) speed of the ball when it passes through its lowest position
m/s

(b) tension in the string when the ball is at its highest position
N

(c) tension in the string when the ball is at its lowest position

Answer 1

Given that the mass of the ball m=0.540 kg.

The length of the pendulum l=0.830 m.

Let the distance between the highest point and the lowest point is x.

The distance between the highest and lowest point is

  

a) Let the speed when it passing through the lowest point is v.

From the conservation of energy, we can say

  

  

  

  

  

The speed when it passing through the lowest point is 1.476312545 m/s or 1.48 m/s.

b) Let the tension in the string when the ball is at the highest point is T₁.

The tension in the string at the highest point is

  

c) Let the tension in the string when the ball is at its lowest point position is T₂.

The tension in the string at the lowest point is

   The tension in the string when the ball is at its lowest point position is 6.709987126 N or 6.71 N approximately.