Time problem involving Mass and a Pulley?

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SUMMARY

The discussion revolves around a physics problem involving an Atwood's machine scenario with Bob and Cathy, two construction workers, and a keg of nails. The problem requires calculating the total time taken for a series of events involving their fall and the keg's ascent and descent. Key variables include Bob's mass (93.1 kg), Cathy's mass (66.1 kg), the keg's mass (47.1 kg), and the nails' mass (64.1 kg). The solution necessitates the application of kinematic equations and principles of motion to determine the times for each segment of the incident.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with the concept of Atwood's machine
  • Knowledge of mass and weight calculations
  • Ability to analyze motion under gravity
NEXT STEPS
  • Study the kinematic equations for uniformly accelerated motion
  • Learn how to apply the principles of Atwood's machine to solve problems
  • Research the effects of mass on acceleration in pulley systems
  • Explore collision physics and its impact on subsequent motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion, as well as educators seeking to illustrate practical applications of kinematic principles.

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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