- #1

ex81

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## Homework Statement

A worker with a mass of M

_{w}is pulling on a mass-less rope that is attached to a box with a mass of m

_{b}on a friction-less surface. The worker pulls with a constant force starting at rest. The Worker is at x = 0, and the box is at x

_{b}Find the position at which they meet in terms given.

## Homework Equations

x = x

_{i}+ v

_{i}* t + 1/2 a * t

^{2}

F = m * a

## The Attempt at a Solution

Using Newton's laws I know that the force on each object is equal, so

F

_{w}= F

_{b}

x

_{w f}= x

_{w i}+ v

_{w i}* t + 1/2 a * t

^{2}

thus for the worker's side of the equation

x

_{w f}= 1/2 a * t

^{2}

and the box moves

x

_{b f}= x

_{b i}+ v

_{b i}* t - 1/2 a * t

^{2}

thus

x

_{b f}= x

_{b i}- 1/2 a * t

^{2}

since they meet x

_{b f}is equal to x

_{w f}

thus

1/2 a * t

^{2}= x

_{b i}- 1/2 a * t

^{2}

x

_{b i}= 1/2 a

_{w}* t

^{2}+ 1/2 a

_{b}* t

^{2}

2 x

_{b i}= (a

_{w}+ a

_{b}) * t

^{2}

t = √( ( 2 * x

_{b i}) / a

_{w}+ a

_{b})

then taking what I have just solved for time, and plugging that back into the basic kinematic equation to find the distance I get jibberish. So I'm not sure where to go from here.

x

_{meet}= x

_{initial}+ 1/2 a

_{worker}* ( ( 2 * x

_{b i}) / a

_{w}+ a

_{b})