a uniform beam of weight 420 N and length 3.2 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N.
(a) What value of D corresponds to that tension?
m
(b) Give any value for D that won't snap the cable.
m
John, we are not going to work homework or test questions. We will, however critique your work or thinking.
To find the value of D that corresponds to the tension in the cable, we can use the principle of moments, which states that the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about the same point when an object is in equilibrium.
(a) Let's calculate the moments about the hinged point on the left:
Clockwise moment = Tension in the cable × distance from the hinged point to the cable bolt (D)
Anticlockwise moment = Weight of the beam × distance from the hinged point to the center of mass of the beam (length of the beam / 2)
Since the beam is in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments:
1200 N × D = 420 N × (3.2 m / 2)
1200 D = 420 × 1.6
1200 D = 672
D = 672 / 1200
D = 0.56 m
Therefore, the value of D that corresponds to the tension of 1200 N is 0.56 m.
(b) To find any value for D that won't snap the cable, we need to consider the maximum value the tension in the cable can have without snapping it. In this case, the least tension that will snap the cable is given as 1200 N. So any value for D that results in a tension less than 1200 N will not snap the cable.