A large uniform \"butcher block\" rests on two supports and has a weight hanging

Question

A large uniform "butcher block" rests on two supports and has a weight hanging from its end. The block has a mass of 100 kg and a length of 2 meters. If L = 1.63 meters and the hanging weight is 192 newtons, what is the force on the left support to the nearest newton?

^^ This part of the question i know how to do, I am having problems with the follow up questions:

1) If the hanging weight is 59 newtons, what is the minimum value for L for the configuration to remain stable to the nearest hundredth of a meter?

2) What is the minimum value for the hanging weight to the nearest tenth of a kilogram if L = 1.24 meters and the configuration is to remain stable?

Explanation / Answer

The answer to the first part is: sumTorque (about left support) = 0 -(1m)(100kg)(9.8m/s^2) - (2m)(192 N) + 1.63(Fr) = 0 Fr= 836.81N SumFy = 0 Fl - (100kg)(9.8M/s^2) - 192N + Fr = 0 Fl = 335.19N

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