Question

The bob of a simple pendulum is imparted a velocity of 5 m s^-1 when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air? (Take g = 10 m s^-2).

April 24, 2024

Answer

Energy lost = 0.6 × KE

kinetic energy = $1\over 2$ × mass × (velocity)²

= $1\over 2$ × mass × 5²

Energy lost = 0.6 × $1\over 2$ × mass × 5²

⇒ Energy Available = 0.4 × $1\over 2$ × mass × 5²

Applying the rule for the conservation of energy we get,

Kinetic energy available = potential energy

⇒ 0.4 × $1\over 2$ × mass × 5² = mass × gravity × height

⇒ $1\over 2$ × 5 × 5 × 0.4 = 10 × h

⇒ 10h = $1\over 2$ × 10

⇒ 10h = 5

⇒ h = 0.5 m

∴ Maximum vertical height reached = 0.5m

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The bob of a simple pendulum is imparted a velocity of 5 m s-1 when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air? (Take g = 10 m s-2).

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The bob of a simple pendulum is imparted a velocity of 5 m s^-1 when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air? (Take g = 10 m s^-2).