Solving Rotational Statics: Force Left Support Exerts on Beam

[ryanmk54]

Homework Statement

A gymnast with mass m1 = 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 118 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
What is the force the left support exerts on the beam?

Homework Equations

Sum of Torques = 0
Sum of Forces = 0
F = ma
T = rf

The Attempt at a Solution

I set the second beam as the axis of rotation since that is an unknown quantity.
m1 = man
m2 = beam
N1 = first support
N2 = second support

The equations I got are:
m1*g + m2*g - N1 - N2 = 0
-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0

Using the second equation, I solved for N1 = 2Lm1g+Lm2g/2 = 7406.55 which is wrong

What am I doing wrong?

 

[SteamKing]

Homework Statement

A gymnast with mass m1 = 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 118 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
What is the force the left support exerts on the beam?

Homework Equations

Sum of Torques = 0
Sum of Forces = 0
F = ma
T = rf

The Attempt at a Solution

I set the second beam as the axis of rotation since that is an unknown quantity.
m1 = man
m2 = beam
N1 = first support
N2 = second support

The equations I got are:
m1*g + m2*g - N1 - N2 = 0
-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0

Using the second equation, I solved for N1 = 2Lm1g+Lm2g/2 = 7406.55 which is wrong

What am I doing wrong?

Check your algebra for solving this equation:

-2L*m1*g/3 + LN1/3 - L*m2g/6 = 0

 

[ryanmk54]

Thank you. I was able to solve it correctly. I'll have to watch out for algebra mistakes.