# a horizontal spring with a 3.00 kg mass is compressed 40.0 cm by 30.0N of force. a Determine the spring constant (in N/m) b Determine the work done in compressing the spring

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### 1 Answer

a) Hooke’s law gives the force (F) a spring exerts on an object attached to it with the following equation:

`F = -kx ` where k is called the spring constant and x is the distance the spring is stretched or compressed away from its equilibrium or rest position.The minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring.

Looking only at the magnitudes and therefore omitting the negative sign, we get:

`k=F/x`

Here, F= 30.0N and x= 40.0 cm=0.4 m

Plugging in the values we get:

`k=F/x`

`rArr k=30.0/0.4` N/m

`rArr k=75` N/m

**Therefore, the spring constant is 75 N/m.**

b) The magnitude of the work done to compress the spring a distance x is given by :

`W=1/2kx^2`

`rArr W=1/2*75*(0.4)^2=6 J`

**Therefore, the work done in compressing the spring is 6 J.**

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