CBSE (Science) Class 11CBSE
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Solution - The Potential Energy Function for a Particle Executing Linear Simple Harmonic Motion is Given By V(X) =Kx2/2, Where K Is the Force Constant of the Oscillator. For K = 0.5 N M–1, the Graph Of V(X) Versus X Is Shown in Fig. 6.12. Show that a Particle of Total Energy 1 J Moving Under this Potential Must ‘Turn Back’ When It Reaches X = ± 2 M - CBSE (Science) Class 11 - Physics

Question

The potential energy function for a particle executing linear simple harmonic motion is given by V(x=kx2/2, where is the force constant of the oscillator. For k = 0.5 N m–1, the graph of V(x) versus is shown in Fig. 6.12. Show that a particle of total energy 1 J moving under this potential must ‘turn back’ when it reaches = ± 2 m

Solution 1

Here, force constant k = 0.5 Nm-1 and total energy of particle E = 1J. The particle can go up to a maximum distance xm, where its total energy is transformed into elastic potential energy.

`1/2 kx_m^2 =E`

`=> x_m =sqrt((2E)/K) = sqrt((2xx1)/(0.5)) = sqrt4 = +- 2m`

Solution 2

Total energy of the particle, E = 1 J

Force constant, k = 0.5 N m–1

Kinetic energy of the particle, K = `1/2mv^2`

According to the conservation law:

E = V + K

`1=1/2 kx^2 + 1/2 mv^2`

At the moment of ‘turn back’, velocity (and hence K) becomes zero.

`:. 1 = 1/2kx^2`

`1/2xx0.5x^2 = 1`

`x^2 = 4`

`x =+-2`

Hence, the particle turns back when it reaches = ± 2 m.

Is there an error in this question or solution?

APPEARS IN

 NCERT Physics Textbook for Class 11 Part 1 (with solutions)
Chapter 6: Work, Energy and Power
Q: 4 | Page no. 135

Reference Material

Solution for question: The Potential Energy Function for a Particle Executing Linear Simple Harmonic Motion is Given By V(X) =Kx2/2, Where K Is the Force Constant of the Oscillator. For K = 0.5 N M–1, the Graph Of V(X) Versus X Is Shown in Fig. 6.12. Show that a Particle of Total Energy 1 J Moving Under this Potential Must ‘Turn Back’ When It Reaches X = ± 2 M concept: Potential Energy of a Spring. For the courses CBSE (Science), CBSE (Arts), CBSE (Commerce)
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