Physics

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).

Work, Energy & Power

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Answer

Given,

Energy lost = 0.6 x KE

KE = $\dfrac{1}{2}$ x mass x velocity²

Substituting the values we get,

$KE = \dfrac{1}{2} \times mass \times 5^2 \\[0.5em]$

Amount of energy lost,

$\text{Energy lost} = \dfrac{1}{2} \times mass \times 5^2 \times 0.6 \\[0.5em]$

Amount of energy available,

$\text{Energy available} = \dfrac{1}{2} \times mass \times 5^2 \times 0.4\\[0.5em]$

Applying the rule for the conservation of energy we get,

Kinetic energy available = potential energy

$\dfrac{1}{2} \times mass \times 5^2 \times 0.4 = mass \times gravity \times height\\[0.5em] \Rightarrow \dfrac{1}{2} \times 5 \times 5 \times 0.4 = 10 \times height\\[0.5em] \Rightarrow \dfrac{1}{2} \times 5 \times 2 = 10 \times height\\[0.5em] \Rightarrow 5 = 10 \times height\\[0.5em] \Rightarrow height = 0.5m \\[0.5em]$

∴ Maximum vertical height reached = 0.5m

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Physics

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).

Work, Energy & Power

Answer

Related Questions

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1MW. (Take g = 10 m s^-2).

Physics

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).

Work, Energy & Power

Answer

Related Questions

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1MW. (Take g = 10 m s-2).

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).

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1MW. (Take g = 10 m s^-2).