Statics - long rod of linear varying density supported at both ends

[jtulibarri]

A 3.0 m long rod has a density described by = a + bx, where is the density in kilograms per meter of length, a = 5.0 kg/m, b = 5.0 kg/m2, and x is the distance in meters from the left end of the rod. The rod rests horizontally with its ends each supported by a scale. What do the two scales read?


I don't even know how to start this one.

If anyone can show me how to set this up I can solve the rest

 

[learningphysics]

First find the mass of the rod, and the location of the center of mass of the rod...

The measurement the scale reads, is the magnitude of the normal force that the scale exerts...

You can find one of these forces using net torque about the appropriate point = 0...

Then the other force can also be obtained using torque... or using sum of forces in y-direction = 0.