The bob of a pend

The tension at the string, horizontal is T= 8mg

The tension at the string, highest point is T’ = 5mg

The tension at the string, at a 60^o from the normal is T’’= 6.5mg

Given

The horizontal velocity of the pendulum after hit is , and “l” is the length of the pendulum.

Formula Used

The formula for the total energy in terms of kinetic and potential energy is given as

&

where

The is the total energy in terms of kinetic and potential energy, m is the mass of the object, g is the acceleration in terms of gravity and r is the length of the rod/thread attached with the bob, m is the mass of the bob, is the velocity of the bob.

Explanation

(a). Let the velocity of the bob at horizontal plane (B) be and the velocity when the bob reaches the lowest point (A) of the bob circle is taken as. Hence, the relationship between kinetic and potential energy be

Therefore, making the tension in the horizontal position as, placing

(b). When the bob reaches at the top of the circle that is opposite to point A the velocity here is taken as . Hence the velocity is

Now taking in the tension when the bob is at height C, the bob also experience the downward force of making the velocity as

(c) The velocity at point D which is at from the normal is taken as, making the velocity as

Therefore, the tension is taken as