A spring is compressed by 0.02m. Calculate the energy stored in the spring if the force constant is 400Nm-1
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Answer:
The answer is 2,416 m/s. Let's jump in.
Explanation:
We do work with the amount of energy we can transfer to objects. According to energy theory:
W = ΔE
Also as we know W = F.x
We choose our reference point as a horizontal line at the block's rest point.<u> At the rest, block doesn't have kinetic energy</u> and <u>since it is on the reference point(as we decided) it also has no potential energy.</u>
Under the force block gains;
W = F.x →
In the second position block has both kinetic and potential energy. Following the law of conservation of energy;
W = ΔE = Kinetic energy + Potantial Energy
W = ΔE =
Here we can find h in the triangle i draw in the picture using sine theorem;
In a triangle
In our situation
→
Therefore
→
Answer:
Explanation:
A mass of 700 kg will exert a force of
700 x 9.8
= 6860 N.
Amount of compression x = 4 cm
= 4 x 10⁻² m
Force constant K = force of compression / compression
= 6860 / 4 x 10⁻²
= 1715 x 10² Nm⁻¹.
Let us take compression of r at any moment
Restoring force by spring
= k r
Force required to compress = kr
Let it is compressed by small length dr during which force will remain constant.
Work done
dW = Force x displacement
= -kr -dr
= kr dr
Work done to compress by length d
for it r ranges from 0 to -d
Integrating on both sides
W =
= [ kr²/2]₀^-4
= 1/2 kX16X10⁻⁴
= .5 x 1715 x 10² x 16 x 10⁻⁴
= 137.20 J