Homework Help: Convert N/m^2 to Newtons, beam problem

1. May 19, 2014

bjorn_v

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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?

Last edited by a moderator: Sep 25, 2014
2. May 19, 2014

Gauss

Hey bjorn,

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

3. May 19, 2014

bjorn_v

No I was not.

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

So it is located 4.000m from the wall.

4. May 19, 2014

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?

5. May 19, 2014

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.

6. May 19, 2014

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.

7. May 19, 2014

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.

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