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A330NEO

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## Homework Statement

A uniform 10-foot-long heavy rope is coiled loosely on the ground. One end of the rope is pulled vertically upward by means of a constant force of 5lb. The rope weighs 1lb/ft. Use Newton's second law to determine a differential equation for the height x(t) of the end above ground level at time t. Assume that a positive direction is upward.

## Homework Equations

The answer says it's [itex] x \frac{d^{2}x}{dt^2} + \left ( \frac{dx}{dt} \right )^{2}+32x=160 [/itex]

## The Attempt at a Solution

Since Newton's second law is F=ma, I tried this:

a(Acceleration) is position x differentiated twice, so [itex]a=\frac{d^{2}x}{dt^2}[/itex]

m=x, and force is 5-x. so, the equation becomes

[itex]5-x=x \frac{d^{2}x}{dt^2}[/itex]

is anything wrong?

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