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If a spring has a constant of #2 (kg)/s^2#, how much work will it take to extend the spring by #62 cm #?

Answer 1

Nathan Ashcroft

#therefore W = 3844 J#

#W = PE = 1/2 kx^2#

#PE = 1/2 kx^2 = 1/2 * 2 * 62^2 = 3844 K#

#therefore W = 3844 J#

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Answer 2

Charlotte Aaron

To calculate the work required to extend the spring, you can use the formula for the work done on a spring:

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

Where:

( W ) is the work done,
( k ) is the spring constant, and
( x ) is the displacement from the equilibrium position.

Given ( k = 2 , \text{(kg/s}^2)), and ( x = 0.62 , \text{m} ) (converted from 62 cm to meters), we can plug these values into the formula:

[ W = \frac{1}{2} \times 2 \times (0.62)^2 ]

[ W = \frac{1}{2} \times 2 \times 0.3844 ]

[ W = 0.3844 , \text{J} ]

So, it will take approximately 0.3844 joules of work to extend the spring by 62 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.