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## Homework Statement

There are four masses hanging by a rope from the

ceiling in the simplest arrangement possible, mass 4 is attached by the rope to mass three right above it,

mass three is attached by a rope to mass 2 right above it, mass 2 is attached by the rope to mass 1 right above it

and mass one is attached by the rope to the ceiling. So the masses are hanging vertically from the ceiling attached by the rope.

Two of the tensions and three of the masses have been measured.

We know: T

_{1}T

_{2}m

_{1}m

_{2}m

_{3}Show that the fourth mass can be expressed as

m

_{4}= (m

_{1}T

_{2}/T

_{1}- T

_{2}) - m

_{2}- m

_{3}

## Homework Equations

F = mg

## The Attempt at a Solution

We know that m

_{4}g + m

_{3}g + m

_{2}g = T

_{2}

so m

_{4}= (T

_{2}/g) - m

_{2}- m

_{3}since multiplying the first term by m

_{1}/m

_{1}is the same as multiplying the term by one, we get m4 = (m

_{1}T2/m

_{1}g) - m2 - m3 using the fact that T

_{1}- T

_{2}= m

_{1}g and substituting this equation in the denominator we get m

_{4}= (m

_{1}T

_{2}/T

_{1}- T

_{2}) - m

_{2}- m

_{3}QED

Is this right? Did I answer the question properly? Just seems like I cheated. If you can point me in the direction of a better answer I'd greatly appreciate it.

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