the figure shows a uniform beam of weight 420 N and length 2.0 m suspended horizontally. On the left it is hinged to a wall, on the right it is supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1100 N. What value of D corresponds to that tension? the figure cant be posted bt its like a right angle triangle on vertical side its wall, base side has the beam and hypotenuse is the string.
To find the value of D that corresponds to the tension of 1100 N, we can start by considering the forces acting on the uniform beam.
The weight of the beam (420 N) acts at its center of mass, which is at a distance of 1.0 m from the hinge (assuming the beam has uniform mass distribution).
The cable exerts an upward force, which we will call T.
Since the beam is in equilibrium (not accelerating), the sum of the forces in the vertical direction must be zero. The vertical forces on the beam include the weight (420 N) and the tension in the cable (T).
Therefore, we can write the following equation:
T - 420 N = 0
This equation tells us that the tension in the cable is equal to the weight of the beam.
However, we are given that the least tension that will snap the cable is 1100 N. So we can modify the equation as follows:
T - 420 N = 1100 N
Now, we can solve for T:
T = 1100 N + 420 N
T = 1520 N
Now that we know the tension in the cable is 1520 N, we can use it to find the value of D.
The torque about the hinge due to the tension in the cable must balance the torque about the hinge due to the weight of the beam.
The torque about the hinge due to the tension in the cable is given by T * D.
The torque about the hinge due to the weight of the beam is given by (420 N) * (1.0 m).
Since the beam is in equilibrium, these two torques must be equal:
T * D = (420 N) * (1.0 m)
Now we can substitute the value of T (1520 N) into the equation:
1520 N * D = (420 N) * (1.0 m)
Simplifying the equation gives:
1520 N * D = 420 N * 1.0 m
D = (420 N * 1.0 m) / 1520 N
D = 0.276 m
Therefore, the value of D that corresponds to the tension of 1100 N is 0.276 m.