A 120-cm-wide sign hangs from a 5.3kg , 200-cm-long pole. A cable of negligible

Question

A 120-cm-wide sign hangs from a 5.3kg , 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in the figure(Figure 1) .

Figure 1:

What is the maximum mass of the sign if the maximum tension in the cable without breaking is 390N ?

120-cm-wide sign hangs from a 5.3kg , 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in the figure(Figure 1) . Figure 1: What is the maximum mass of the sign if the maximum tension in the cable without breaking is 390N ?

Explanation / Answer

mass of the long pole m = 5.3 kg

length of the long pole L = 200 cm = 2 m

tension in the cable T = 390 N

length of the sign board L' = 120 cm = 1.2 m

angle theta = tan-1(250 cm / 200 cm) = 51.340

weight of the long pole W = F = mg

weight of the sign board W' = F' = m'g

the net torque taking pivot at point O is

sigma T = -(F)(100 cm) -(F')(140 cm) + L (T sin theta) = 0

-(F)(100 cm) -(F')(140 cm) + L (T sin theta) = 0

L (T sin theta) = (mg)(100 cm) + (m'g)(140 cm) = 0

(200 cm)(390 N)(sin 51.340) = (5.3 kg)(9.8 m/s2)(100 cm) + (m')(9.8 m/s2)(140 cm)

(2 m)(390 N)(sin 51.340) = (5.3 kg)(9.8 m/s2)(1 m) + (m')(9.8 m/s2)(1.40 m)

(609.08) = 51.94 + (13.72 * m')

mass m' = 40.61 kg

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