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Q.7

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 414

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Short Answer

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

See the step by step solution

Step by Step Solution

Step 1: The expression of total energy

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.

Step 2:The expression of total kinetic energy

Obtain a relation between maximum speed and total kinetic energy.

Equate the expression and

Step 3: Calculation of total energy

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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