A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 1502915 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.7 kg and the sign has a mass of ms = 17.1 kg. The length of the beam is L = 2.75 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is = 33.4°. What is the tension in the wire? What is the net force the hinge exerts on the beam? The maximum tension the wire can have without breaking is T = 936 N. What is the maximum mass sign that can be hung from the beam?
Explanation / Answer
1) Sum the moments about the base of the beam:
M = 0 = (17.1kg+½*6.7kg)*9.8m/s²*2.75m*cos33.4º - T*(2/3)*2.75m*sin33.4º
0 = 551.12N·m - T * 1.53m
T = 360.20 N
2) horizontally, Fx = 360.20 N
vertically, Fy = (17.1 + 6.7)kg * 9.8m/s² = 233.24 N
net F = (Fx² + Fy²) = 429.12 N
3) 0 = (M+½*6.7kg)*9.8m/s²*2.75m*cos33.4º - 936N*(2/3)*2.75m*sin33.4º
0 = (M + 3.35kg)*22.49m²/s² - 944.62N·m
M + 3.35kg = 944.62N·m / 22.49m²/s² = 42.00 kg
M = 38.65 kg