Torque from beam and worker on cantilever beam

[Blistex]

Homework Statement

A 4.0m long, 500kg steel beam extends horizontally from where it has been bolted to the framework of a new building under construction. A 70kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the point where the beam is bolted in place?

M1 = 500kg
M2= 570kg
X1 = 0m
X2 = 4m
g = 9.8 m/s²

Homework Equations

T = Mgx_cm

Where Mg is the net gravitational force on the object and X_cm is the moment arm between the rotational axis and the center of mass.

The Attempt at a Solution

I thought this problem would quite simple but I think there might be an error in my reasoning.

I start by calculating the center of mass. {(500kg)(0m) + (570kg)(4m)}/1070kg = 2.13m
So the CM is 2.13 from the fulcrum.

Next I substitute the given values into the equation. T = (500kg + 70kg)(9.8m/s²)(2.13m) = 11902NM or 11.9k Nm.
This should be the torque about the fulcrum.

Thanks for the help the book says 12.5k Nm. So far it's been pretty spot on this far.

 

[tiny-tim]

Welcome to PF!

Hi Blistex! Welcome to PF!

A 4.0m long, 500kg steel beam extends horizontally from where it has been bolted to the framework of a new building under construction. A 70kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the point where the beam is bolted in place?
…
M1 = 500kg
M2= 570kg

erm …

where did 570 come from? ​

(and anyway, you don't need to find the centre of mass, just find each torque separately, and add! )

 

[Blistex]

Thank Tim!

Given T_grav = Mgx_cm

I summed the individuals particles that had torque on the object. I.e only the worker. which amounted to dsin(x)*m*g = -2744Nm

The other side of the equation asks for the mass relative to the center of rotation, that's where my miscalculation entered. Whereas the center of mass is simply 4m/2, the center of the length of the beam. I had thought the weight of the worker would cause the CM to shift farther towards the worker. I guess that's what relative meant. After plugging in the rest of the variables I was able to solve it.

Thanks for your help.