Q.7

Expert-verifiedFound in: Page 414

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A block oscillating on a spring has a maximum speed of . What will the block's maximum speed be if the total energy is doubled? Explain.

The block's maximum speed on doubling the total energy is

The expression for total energy of a block oscillating on a spring is,

.......(1)

Here, is spring constant and is amplitude of oscillation.

Equate the total kinetic energy with total kinetic energy at the mean position.

......(2)

Here, is mass of the block and is maximum speed.

Obtain a relation between maximum speed and total kinetic energy.

Equate the expression and

Calculate the block's maximum speed on doubling the total energy.

Substitute for and for in the above equation

.

Whenever the total energy is twice, the block's maximum speed is .

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