A 120- c m -wide sign hangs from a 5.5 k g , 200- c m -long pole. A cable of neg
ID: 2270500 • Letter: A
Question
A 120-cm-wide sign hangs from a 5.5kg , 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in the figure(Figure 1) .
1.What is the maximum mass of the sign if the maximum tension in the cable without breaking is 330N ?
A 120-cm-wide sign hangs from a 5.5kg , 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in the figure(Figure 1) . What is the maximum mass of the sign if the maximum tension in the cable without breaking is 330N ?
Explanation / Answer
The angle of the cable is 51.340 degrees.
ArcTan(250 / 200) = 51.340
If the tension in the cable is to kept at or below 330 Newtons, the vertical component of the tension must not exceed 257.68 Newtons.
Sin(51.340) * 330 = 257.68
The weight of the pole is 53.9 Newtons.
...and half of that weight is applied to the vertical component of the tension on the cable.
We can increase the vertical component by an additional 230.73 Newtons without breaking the cable.
257.68 - 53.9 / 2 = 230.73
For each kilogram of sign that we hang, 9.8 Newtons of weight are added to the system.
...and 70% of each 9.8 Newtons of weight is added to the cabled end of the pole.
(80 + 120 / 2) / 200 = 0.700 = 70%
So, for each kg of sign an additional 6.86 Newtons is added to the vertical component of the tension of the cable.
9.8 * 0.7 = 6.86
The sign can have a mass as high as 33.634 kg without breaking the cable.
230.73 / 6.86 = 33.634
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