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notsponge [240]
3 years ago
6

The spring is now compressed so that the unconstrained end moves from x=0 to x=L. Using the work integral W=∫xfxiF⃗ (x⃗ )⋅dx⃗ ,

find the work done by the spring as it is compressed. Express the work done by the spring in terms of k and L?

Physics
1 answer:
Savatey [412]3 years ago
4 0

solution:

the spring force exerted by spring with spring constant k is given by

F(x)=-kx

where k is spring constant

and x is deformation of spring

in order to calculate word done by the spring

W=\int\limits^L_0 {} \, dW

the work done by the spring as it is compressed from x=0 to x=L

W=-kx^2/2

inserting the limits x=0 and x=L

we get work done in terms of k and L

ANSWER

W=-kL^2/2

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v_1(t)=80.6\dfrac{\rm m}{\rm s}+\left(3.90\dfrac{\rm m}{\mathrm s^2}\right)t

The rocket then reaches an altitude of 1150 m at time <em>t</em> such that

1150\,\mathrm m=\left(80.6\dfrac{\rm m}{\rm s}\right)t+\dfrac12\left(3.90\dfrac{\rm m}{\mathrm s^2}\right)t^2

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At this time, the rocket attains a velocity of

v_1(11.2\,\mathrm s)=124\dfrac{\rm m}{\rm s}

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y_2(t)=1150\,\mathrm m+\left(124\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2

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That is, the rocket has a velocity of 196 m/s in the downward direction as it hits the ground.

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