Question

Potential energy of particle of mass 2 kg oscillating
on x-axis is given as U = (x - 2)2 – 10.
The total energy of oscillation is 26 J. Find the
maximum speed of particle.
(1) 4 m/s
(2) 8 m/s
(3) 13 m/s (4) 6 m/s​

Answer 1

The maximum speed of the particle is 6 m/s.

(4) is correct option.

Explanation:

Given that,

Mass = 2 kg

Total energy = 26 J

Potential energy is  given by

$U=(x-2)^2-10$

$U=x^2+4-2x-10$...(I)

For maximum speed kinetic energy should be maximum.

$U=(x-2)^2-10$

$\dfrac{dU}{dx}=2(x-2)$

$\dfrac{dU}{dx}=2x-4$...(II)

Now, $\dfrac{dU}{dx}=0$

Put the value in the equation (II)

$2x-4=0$

$x=2$

Put the value of x in equation (I)

$U=4+4-8-10$

$U=-10\ J$

We need to calculate the maximum speed of the particle

Using formula of total energy        

$T.E=U+K$

$26=-10+\dfrac{1}{2}\times2v^2$

$v^2=36$

$v=6\ m/s$

Hence, The maximum speed of the particle is 6 m/s.

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Topic : Potential energy

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