Solving Rotational Statics: Force Left Support Exerts on Beam

• ryanmk54
In summary, the problem involves determining the force exerted by the left support on a balance beam with a gymnast of mass 46 kg standing on it. Using the equations of sum of torques and sum of forces, the correct solution for the force exerted by the left support was found to be 7406.55 N.
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?

ryanmk54 said:

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

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

What is rotational statics and how is it different from linear statics?

Rotational statics is a branch of mechanics that deals with the equilibrium of objects under rotational forces. It differs from linear statics, which deals with the equilibrium of objects under purely linear forces.

What is the force left support exerts on a beam?

The force left support exerts on a beam is the external force acting on the left end of a beam, which is necessary to maintain the beam in rotational equilibrium.

How do you solve for the force left support?

To solve for the force left support, you need to first identify all the external forces acting on the beam, including any applied forces and the weight of the beam itself. Then, using the principles of rotational equilibrium, you can set up and solve equations to determine the magnitude and direction of the force left support.

What factors affect the force left support on a beam?

The force left support on a beam is affected by the weight and length of the beam, as well as the position and magnitude of any external forces acting on the beam. The angle at which the beam is supported and the material properties of the beam can also impact the force left support.

Why is it important to understand rotational statics and solve for the force left support?

Understanding rotational statics and being able to solve for the force left support is crucial for designing and analyzing structures that are subject to rotational forces, such as bridges and cranes. It ensures that these structures are stable and can withstand the forces acting upon them, ensuring the safety and functionality of the structure.

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