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: T1 T2 m1 m2 m3 Show that the fourth mass can be expressed as
m4 = (m1T2/T1 - T2) - m2 - m3
F = mg
The Attempt at a Solution
We know that m4g + m3g + m2g = T2
so m4 = (T2/g) - m2 - m3 since multiplying the first term by m1/m1 is the same as multiplying the term by one, we get m4 = (m1T2/m1g) - m2 - m3 using the fact that T1 - T2 = m1g and substituting this equation in the denominator we get m4 = (m1T2/T1 - T2) - m2 - m3 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.