Solving the Simpsons' Eviction Homework Statement

[shimizua]

Homework Statement

The Simpsons are sitting on their 2 meter-long family sofa. They are being evicted but refuse to leave their sofa. The police send two movers to lift the couch. Each grabs one end.< /sub>
M Homer = 100 kg
M Santa's Little Helper =20kg,
MMarge= 60 kg,
MLisa=30kg,
MSnowball=5kg,
MMaggie=10kg,
MBart=40kg,
Mcouch=100 kg
The distance of each occupant from the left end of the couch is xHomer=0.25m
xSanta's Little Helper0.50m,
xMarge=0.75m,
xLisa=1.00m,
xSnowball=1.25m,
xMaggie=1.50m,
xBart=1.75m,
Xcouch= 1 m
What force do the two movers need to apply at x=0m and x=2.00m to lift the couch and hold it steady 1 meter off the floor? The mover on the left drops his end. The mover on the right continues to hold his end steady 2 meters off the floor. Hint: calculate the net torque about the right end of the couch. The moment of inertia of the couch that rotates about one end is 1/3ML2. Determine the initial angular acceleration of the couch.Use the value for the initial angular acceleration to determine the initial vertical acceleration of the couch underneath Homer and Marge. Do either of them float off the couch as it rotates from underneath them?One of the movers is very strong so he decides to pick the sofa up by himself. Where would he need to lift it so that it does not rotate out of his grasp? Beneath what location X from the left end would he need to lift so that the couch does not rotate when he picks it up.

Homework Equations

Well so far all that i can come up with is that each will need to pick up 182.5kg. i am not sure about really anything else, except for maybe the first part about the force the two movers need at x=0 and x=2. would i just do F=ma? other then that i am pretty lost

The Attempt at a Solution

 

[LowlyPion]

Hint: What is the definition of Torque?

Here is a link that might help:

http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html#equi

 

[mgb_phys]

This is very similair to this question
https://www.physicsforums.com/showthread.php?t=270204

 

[janine5486]

I have this exact problem for homework as well. HELP!

 

[LowlyPion]

I have this exact problem for homework as well. HELP!

Welcome to PF.

I suggest you follow the links that have been supplied.

There are two important conditions that need to be met.

Σ Forces holding the couch up and Springfield inhabitants weighing it down = 0

Σ Torque about either end must also be 0.