Physics question on Newton's Second Law

Aurora2000 · Jan 16, 2012, 02:22 AM

The candelier generates a force $F=mg=66.5kg \times 9.81m/s^2$ due to gravity. The 3 wires
must balance this force in order to create an equilibrium. Thus the combined force on the 3 wires is
exactly $F$ . As the problem tells you that the tension on each wire is the same, then you have that each wire must have tension $F/3$ .

ebaines · Jan 16, 2012, 07:23 AM

Quote:

Originally Posted by Aurora2000

each wire must have tension $F/3$ .

Not quite right. This would be true if all 3 wires were vertical, but they're not. Given that the chandelier is hanging 1.5m below the ceiling, and each wire is 2m long, this tells you that the wires are at an angle $\theta$ to the vertical, where

$cos\theta = \frac {1.5} 2$ .

The vertical component of force in each wire must be 1/3 the weight as you show, but the tension in them is greater than that, as there is both a horizontal and vertical component of tension in the wire. So:

$<br /> T = \frac {W/3 } {\cos(\theta) }<br />$

where W = the weight of the chandelier, in Newtons.

Aurora2000 · Jan 16, 2012, 09:29 AM

Yes, ebaines is right, I have not considered wire length.

seancoakley · Jan 16, 2012, 12:32 PM

OK, thank you for your answers.
So, I hope I've got this right.
If the 3 wires were all vertical, the problem would be easier to solve, since all you would have to do would be to work out the weight of the Chandelier, which I calculate to be 652.37 Newtons. Then, in order for equilibrium to occur (i.e the Sum of the forces = 0), then each wire would have a tension of 217.46 Newtons.
However, as ebaines points out, each wire is at an angle to the vertical, which I calculate to be 41.4 degrees.
Thus, the tension in each wire would be greater than 217.46 Newtons. If 217.46 Newtons is the vertical, then:
cos 41.4 = 217.46 divided by T
(i.e. cos theta (41.4) = adjacent (217.46) divided by the hypotenuse (T)).
Therefore, T = 217.46 divided by 0.75 = 289.89 Newtons.
Hope I did this right!!!

Physics question on Newton's Second Law

Add your answer here.

Check out some similar questions!