Convert N/m^2 to Newtons, beam problem

[bjorn_v]

Homework Statement

I want to convert 110.0 x 10^6 N/m^2 to Newtons. How do I do this?

Reason: I have the following problem and the following question to answer:

P: A heavy mass is supported by a beam-cable system as shown in the figure. The beam is 5.000 m long with a mass of 36.00 kg. The aluminum cable is 8.000 m long with a circular cross section and a diameter of 0.8200 cm. The beam and cable are attached to the wall. A heavy mass is 400.0 kg and is hanging at a point 4.000 m
from the wall.

Q: What is the maximum mass that this system can support before the cable breaks?

(Assume the mass of the cable is negligible
Assume the cable that connects the mass to the beam does not stretch
Young's modulus for aluminum is 70.00 x 109 N/m^2
The breaking strength of aluminum is 110.0 x 106 N/m^2)

Based on this video ( ) I know how to solve the problem, except only if the units are in plain Newtons. So how do I convert them?

OR, if converting is not possible, how do I solve this problem with N/m^2?

Homework Equations

The Attempt at a Solution

$$T_n=T_1+T_2+T_3+T_4$$
$$0=0-2.500*36.00*9.81-4.000*m*9.81+5*F_4$$
So I want to find m.
$$F_4=T*\sinθ$$
$$F_4=?*\sin(\arcsin(\frac{\sqrt{39}}{8}))$$

I know that the breaking strength of aluminum is 110.0 x 106 N/m^2, but how do I convert that to Newtons so I can solve for F₄?

Thanks in advance!

 

[Gauss]

Hey bjorn,

Were you given an answer to check your work with?

EDIT: Also do you know where the mass is located on the beam?

 

[bjorn_v]

Hey bjorn,

Were you given an answer to check your work with?

EDIT: Also do you know where the mass is located on the beam?

No I was not.

Also I forgot to include part of the question. I have updated it with the following information:

A heavy mass is 400.0 kg and is hanging at a point 4.000 m from the wall.

So it is located 4.000m from the wall.

 

[Matterwave]

You have to use your circular cross section information. The thicker the wire, the more force the wire can take before it breaks. How do you think you can use this information?

 

[Gauss]

Remember that Torque = F*R (dot product), and the overall torque of the system has to be 0, otherwise the system would be in movement.

 

[dauto]

Newtons cannot be converted to N/m² because they are different kinds of units used to measure different things. But the stress (measured in N/m²) can be CALCULATED from the force and the cross section area.

 

[bjorn_v]

Based on what you all have said, I figured I could get a Newton value by multiplying the breaking strength by the cross-sectional area of the wire. Cross-sectional area would be m² so the units would cancel out.

$$F_4=110.0*106*(\frac{0.0082}{2})^2*\pi*\frac{\sqrt{39}}{8}=45347.42$$
$$-4.000*m*9.81=0-2.500*36.00*9.81+5*45347.42$$
$$m=\frac{-2.500*36.00*9.81+5*45347.42}{-4.000*9.81}$$
$$m=5755.71$$