Tension Pole
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Physics, motion - What is the tension in the wire?
A wire is very tightly stretched horizontally between two poles 4 meters apart. A bird lands on the centre of the wire, depressing it by a vertical distance of 4cm. What is the tension in the wire?
Ah dangit... forgot to mention the birds weight.
It's 4 kg, sorry.
Oh, and the actual answer to the question is 1000 N.
I just need to know how to work it out.
Thankyou.
Let m be the mass of the bird, and T be the tension in each part of the wire.
The vertical forces on the bird are:
Weight: W = mg
Force of each half of the wire: F = Tsin(theta)
Thus, 2F = W, so 2Tsin(theta) = mg.
Therefore, T = mg/2sin(theta)
Since half of the wire is 2 m long and the height it was depressed is 4 cm, sin(theta) = (4 cm)/(2 m) = 1/50
So, T = 25mg, or 25 times the weight of the bird.
EDIT:
Since the bird weighs 4kg, using g = 10 m/s^2, the answer is:
T = 25mg = 25(4 kg)(10 m/s^2) = 1000 N
