A 27-kg chandelier hangs from a ceiling on a vertical

[hitemup]

Homework Statement

A 27-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire. What horizontal force would be necessary to displace its position 0.15m to one side?

Homework Equations

[/B]
F*x = m*g*h

The Attempt at a Solution

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I tried to find the height the chandelier elevates. With the pythogorean theorem, 4 becomes hypothenus, and 0.15 becomes cathetus.

x^2 + 0.15^2 = 4^2
x = 3.99718651

h = 4 - 3.99718651
h = 0.00281349

Fx = mgh

F*0.15 = 27*9.8*0.00281349
F = 4.96299636

When you multiply my result with 2, you get 9.92599272, which is the correct answer according to the book.(9.9N)

 

[NTW]

The horizontal force that you seek grows with the deviation of the lamp from the vertical. It's as if you pushed a weight up a curved, concave slope... The push you need at different points is different...

 

[gneill]

mgh yields a change in gravitational potential energy, not a force.

If you draw out the scenario you should be able see similar triangles that you can use to relate the forces with the geometry:

 

[hitemup]

mgh yields a change in gravitational potential energy, not a force.

If you draw out the scenario you should be able see similar triangles that you can use to relate the forces with the geometry:

Yes I got the correct answer now, 4/(0.15) = mg/F

mg = 27*9.8 = 264.6
F = 9.9225

I thought of mgh because I believed the work we've done (Fx) must be equal to the change in energy. But what confuses me here is the fact that when you multiply my wrong answer with 2, it gives the exact answer. I guess, like NTW's said, the force is not constant, is it?

 

[gneill]

Yes I got the correct answer now, 4/(0.15) = mg/F

mg = 27*9.8 = 264.6
F = 9.9225

That's actually not right. Neither mg nor F are on the hypotenuse of the force triangle, yet you've used 4 (the hypotenuse of the geometry triangle) in the similarity ratio. Your answer may be very close to right due to the small displacement (0.15 m) compared to the wire length, so y in my diagram is almost equal to 4. But it's not exactly 4. If the displacement were larger the error would be larger.

I thought of mgh because I believed the work we've done (Fx) must be equal to the change in energy. But what confuses me here is the fact that when you multiply my wrong answer with 2, it gives the exact answer. I guess, like NTW's said, the force is not constant, is it?

Right. The force is not constant. In fact it grows without bound as the displacement approaches the wire length. That is to say, there's no finite force, applied strictly horizontally, that could hold the chandelier out horizontally.