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PhysicsW.E.P.Conservative force & potential energyMedium2 minPYQ_2020

PhysicsMediumnumerical

A block of mass $2 k g$ is kept at the origin at $t = 0$ and is having velocity $4 \sqrt{5} m s^{- 1}$ in the positive $x$ -direction. The only force on it is a conservative and its potential energy is defined as $U = - x^{3} + 6 x^{2} + 15$ . Its velocity when the force acting on it is minimum (after the time $t = 0$ ) is -

Answer:

8.00

Solution:

At $x = 0$

$K = \frac{1}{2} \times 2 \times 80 = 80 J$ and $U = 15 J$

$∴ E = K + U = 95 J$

$F = \frac{- d U}{d x} \Rightarrow F = 3 x^{2} - 12 x$

For $F = m i n i m u m, \frac{d F}{d x} = 0$

$\Rightarrow x = 2 m$

At $x = 2 m$

$E = K + U$

$\Rightarrow 95 = \frac{1}{2} \times 2 \times v^{2} + (- 8 + 24 + 15)$

$\Rightarrow v = 8 m s^{- 1}$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Conservative force & potential energy

⏱ 2mℹ️ Source: PYQ_2020

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