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Chapter 15: Q.6 (page 414)

A block oscillating on a spring has an amplitude of 20cm. What will the amplitude be if the total energy is doubled? Explain.

Short Answer

Expert verified

The new amplitude of the block when the total energy is doubled after rounding off to three significant figures is 28.3cm.

Step by step solution

01

Expression for the total energy  

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

E=12kA2

Here, kis the spring constant and Ais the amplitude of the block.

02

Amplitude of the block 

Rewrite the equation E=12kA2for A

A=2Ek

From the above relation, it is clear that the amplitude of the block is directly proportional to square root of its total energy.

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03

Calculation for new amplitude 

Let A'be the new amplitude of the block. Thus, the expression for the new amplitude of the block is,

A'A=E'E

A'=AE'E

Substitute 2Efor E'and 20cmfor A

A'=(20cm)2EE

A'=28.284cm

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