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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 #94 cm #?

Answer 1

Layla Ahmed

The work is #=1.77J#

The amount of work completed is equivalent to the spring's potential energy.

#W=1/2kx^2#

The spring constant is #k=4kgs^-2#

The extension is #x=0.94m#

The task is

#W=1/2*4*0.94^2=1.77J#

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Answer 2

Elena Albarran

To calculate the work required to extend the spring, you can use the formula for the work done by a spring, which is given by ( W = \frac{1}{2} k x^2 ), where ( k ) is the spring constant and ( x ) is the displacement from the equilibrium position.

Given that the spring constant ( k ) is ( 4 , \text{kg}/\text{s}^2 ) and the displacement ( x ) is ( 94 , \text{cm} ), first, convert the displacement to meters: ( 94 , \text{cm} = 0.94 , \text{m} ).

Then, substitute the values into the formula:

[ W = \frac{1}{2} (4) (0.94)^2 ]

[ W = \frac{1}{2} (4) (0.8836) ]

[ W = 2 \times 0.8836 ]

[ W = 1.7672 , \text{J} ]

So, it will take ( 1.7672 , \text{J} ) of work to extend the spring by ( 94 , \text{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.