a 10-m uniform beam of weight 100N is supported by two ropes at the ends. If a 400N erson sits at 2.0 m from the left end of the beam, what is the tension in the right rope?
Sum the moments about any point. I will do it from the left end.
100N*5m+400N*2m-Tright*10=0
solve for Tright.
Now, sum the forces vertically.
Tleft+Tright-100N-400N=0 solve for Tleft.
130 N
A 10 m long uniform beam weighing 100 N is supported by two ropes at the ends as shown. If a 400 N person sits at 2.0 m from one end of the beam, what are the tensions in thr ropes
To find the tension in the right rope, we can use the principle of equilibrium. Since the beam is in a state of equilibrium, the sum of the forces acting on it must be zero.
Let's break down the problem step by step:
Step 1: Determine the forces acting on the beam
- Weight of the beam: The beam has a weight of 100N acting downward from its center. This weight can be considered as acting at the midpoint of the beam.
- Tension in the left rope: The left rope provides an upward force to counterbalance the weight of the beam.
- Tension in the right rope: The right rope also provides an upward force to counterbalance the weight of the beam and the additional weight of the person.
Step 2: Calculate the forces
Since the beam is uniform, the weight of the beam acts at the midpoint, which is 5 meters from the left end of the beam. So, the weight of the beam can be split equally between the left and right sides, which means that each side carries a weight of 50N.
The total weight supported by the right rope is the weight of the beam (50N) plus the weight of the person (400N). So, the total weight on the right side is 450N.
Step 3: Apply the principle of equilibrium
To find the tension in the right rope, we need to find the force needed to counterbalance the total weight on the right side of the beam.
Since the beam is in equilibrium, we can write the equation:
Force on the left side = Force on the right side
Tension in the left rope = Tension in the right rope + Weight on the right side
Substituting the values we have:
50N = Tension in the right rope + 450N
Step 4: Solve for the tension in the right rope
To find the tension in the right rope, we can rearrange the equation:
Tension in the right rope = 50N - 450N
Tension in the right rope = -400N
The negative sign indicates that the tension in the right rope is acting in the opposite direction (upward) to balance the forces. However, tension is always positive in magnitude, so we can take the absolute value.
Therefore, the tension in the right rope is 400N.