Time problem involving Mass and a Pulley?

AI Thread Summary
The discussion revolves around a physics problem involving two construction workers, Bob and Cathy, who accidentally fall while raising a keg of nails using a pulley system. The scenario details their masses and the keg's mass, leading to a series of events where they collide with the ground and the pulley. The problem requires calculating the time taken for each phase of the accident, but the original poster struggles to find the necessary formulas. Suggestions include using principles from an Atwood's machine to analyze the motion. The thread emphasizes the need for clear equations to solve the timing of each event in the sequence.
cal04
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Homework Statement



Bob and Cathy,two construction workers on the roof of a 20m highbuilding,are about to raise a keg of nails from the ground by means of a light rope which passes over a light and frictinless pulley.

Bob’s mass= M1=93.1kg
Cathy’s mass=M2=66.1kg
The keg’s mass=M3=47.1kg
The nails mass=M4=64.1kg

As they cast off the rope, both workers slip off the roof and the following unfortunate sequence of events takes place. Hanging together on the rope Bob and Cathy strike the ground just as the keg hits the pulley. Unnerved by his fall, bob let's go of the rope and watched in stunned amazement as Cathy ascends rapidly until she blips her head on the pulley, But gamely hangs on to the rope. However, when the keg hits bib on the head, the bottom breaks, the nails spill out, and the empty keg now begins a rapid ascent as Cathy returns to the ground. As the keg hits the pulley Cathy is a little stunned as she lies on bob and let's go of the rope only to be hit on the head one last time as the kegs makes its final descent. Ignoring the possibility of mid air collisions, which only ass insult to injury, how long did it take this industrial accident to run its course? Assume that all collisions with the ground or pulley serve to start each subsequent motion from rest so that each trip and down begins with zero velocity.
T1=
T2=
T3=
T4=
Total Time=


Homework Equations


I can't find the formulas I need for this problem in order to find all 4 times? Please help I've been looking for formulas on this problem for a minute. Thank you Cal



The Attempt at a Solution

 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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