How Do You Calculate the Mass M and Support Reaction for a Balanced Beam?

[Gwyddel]

Homework Statement

A uniform beam AB of mass 4.5 kg is 1.6 m long. A mass of M kg is attached to end A and a mass of 3 kg is attached to end B. The beam rests horizontally in equilibirum on a smooth support at point C, where AC = 0.5 m.

Calculate the value of M and the reaction of the support at C.

Homework Equations

Torque = F * d

The Attempt at a Solution

Is this correct?

R = reaction of the support at C
acc. due to gravity = 9.8 ms^-2

R - 9.8M - (4.5*9.8) - (3*9.8) = 0
R = 9.8M + 44.1 + 29.4
R = 9.8M + 73.5

Moments about point C.
(0.5*9.8M)-(0.3*44.1)-(29.4*1.1) = 0
4.9M - 13.23 - 32.34 = 0
4.9M = 45.57
M = 45.57/4.9
M = 9.3 kg

R = 9.8M + 73.5
R = 9.8(9.3) + 73.5
R = 164.64 N

 

[Mapes]

Hi Gwyddel, welcome to PF!

I haven't checked your actual calculations in detail, but your approach and equations look great.