A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 1351964 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.3 kg and the sign has a mass of ms = 17.9 kg. The length of the beam is L = 2.7 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 = 31.1°.
1)What is the tension in the wire?
2) What is the net force the hinge exerts on the beam?
3) The maximum tension the wire can have without breaking is T = 1078 N. What is the maximum mass sign that can be hung from the beam?
Explanation / Answer
given,
mb = 6.3 kg
ms = 17.9
L = 2.7 m
theta = 31.1 degree
since the syste is in equilibrium so torque about hinged point will be 0
torque about hinged point = 6.3 * 9.8 * 2.7 / 2 + 17.9 * 9.8 * 2.7 - T * sin(31.1) * (2/3) * 2.7
6.3 * 9.8 * 2.7 / 2 + 17.9 * 9.8 * 2.7 - T * sin(31.1) * (2/3) * 2.7 = 0
tension in the wire T = 599.061 N
net force on the hinge = sqrt(((6.3 + 17.9) * 9.8 - 61.1286 * sin(31.1))^2 + (61.1286 * cos(31.1))^2)
net force on hinge = 212.144 N
6.3 * 9.8 * 2.7 / 2 + m * 9.8 * 2.7 - 1078 * sin(31.1) * (2/3) * 2.7 = 0
maximum mass = 34.7291 kg