Question

A pendulum bob of mass 0.1 kg is suspended by a string of 1m long.The bob is displaced so that the string becomes horizontal and released. Find its kinetic energy when the string makes an angle of (i) 0o, (ii) 30o with the vertical.

Answer 1

Given:

A pendulum bob of mass 0.1 kg is suspended by a string of 1m long.The bob is displaced so that the string becomes horizontal and released.

To find:

KE of Bob when string makes angle of

• 0°

• 30° with vertical.

Calculation:

1st part:

We will apply Conservation of Mechanical Energy:

$\therefore \: KE1 + PE1 = KE2 + PE2$

$= > 0 + mgl = KE2 + 0$

$= > KE2= 0.1 \times 10 \times 1$

$\boxed{ = > KE2= 1 \: joule}$

2nd Part:

we will again apply Conservation of Mechanical Energy:

$\therefore \: \Delta KE = \Delta PE$

$= > KE2 - 0 = mg \{l \cos( {30}^{ \circ} ) \}$

$= > KE2 = mg \{l \cos( {30}^{ \circ} ) \}$

$= > KE2 = 0.1 \times 10 \times \dfrac{ \sqrt{3} }{2}$

$\boxed{= > KE2 = \dfrac{ \sqrt{3} }{2} \: joule}$

Refer to attached diagram.