Question

Exercise of conservation theorems:
the sphere of mass m of the simple pendulum of the figure is released from rest when the string makes an angle β1 with the vertical; Based on this information:
Determine one expression for velocity and another for tension at the lowest point ②.

A pendulum of 61.0 m in length and 0.400 kg of mass is released from rest when the rope is at an angle of 65.0 or vertical. Find the velocity of the sphere and the tension of the string when the sphere is at the lowest point (②).

βι LCos mg

Answer 1

Energy conservation at (1) & (2) At (1) KE = 0 PE = m g (l - l cos beta_1) At (2) KE = 1/ 2 m v^2 PE = 0 (reference level) implies 0 + m g l (l - cos beta_1) = 1 /2 m v^2 + 0 v = squareroot 2 g l (1 - cos beta_1) - (1) putting the values: v = squareroot 2 times 10 times 61 (1 - cos 65) = 26.54 m/s At (2) Draw the FBD T - m g = m v^2/l T = m (g + v^2/L) = 8.61 N