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If a spring has a constant of #4 (kg)/s^2#, how much work will it take to extend the spring by #8 cm #?

Answer 1

Olivia Askew

#W =1/2xxkxxx^2=1/2xx4xx(0.8)^2=1.28J#

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Answer 2

Xavier Adame

The work required to extend the spring by 8 cm is 0.032 Joules.

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Answer 3

Charles Aeschliman

The work required to extend the spring by 8 cm can be calculated using the formula for the potential energy stored in a spring:

[ W = \frac{1}{2}kx^2 ]

Where:

( W ) is the work done,
( k ) is the spring constant (in ( \text{kg}/\text{s}^2 )),
( x ) is the displacement from the equilibrium position (in meters).

Given that ( k = 4 , \text{kg}/\text{s}^2 ) and ( x = 0.08 , \text{m} ) (8 cm converted to meters), we can plug these values into the formula:

[ W = \frac{1}{2} \times 4 \times (0.08)^2 ]

[ W = \frac{1}{2} \times 4 \times 0.0064 ]

[ W = 0.032 , \text{J} ]

So, it will take 0.032 joules of work to extend the spring by 8 cm.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.