A beam of negligible mass of length 3 m is suspended by a string attached to a wall such that the angle between beam and string is 30 degree, and the beam is held horizontal with a sky weight. Find the tension in the string? Find the compression force on its beam? Thanks...
If the beam has no mass, the beam will not fall if the string is cut. So the tension of the string must be...
What does "sky weight" mean? That is a term I have never heard in my engineering lifetims.
To find the tension in the string, we can start by drawing a free-body diagram of the beam.
Step 1: Draw a diagram of the beam suspended by a string attached to a wall. Label the beam as "B," the string as "S," and the angle between the beam and string as 30 degrees.
Step 2: Identify the forces acting on the beam. Since the beam is being held horizontally by a sky weight, we have the weight force acting vertically downward at the center of the beam. Additionally, the tension force in the string will act at an angle of 30 degrees from the vertical (opposite to the angle between the beam and string).
Step 3: Resolve the weight force into its components. The weight force can be broken down into a vertical component (opposite to the tension force) and a horizontal component (balancing the tension force). The vertical component will be equal to the weight of the beam times the sine of the angle between the beam and string (30 degrees). The horizontal component will be equal to the weight of the beam times the cosine of the angle between the beam and string (30 degrees).
Step 4: Set up equilibrium equations for the vertical and horizontal forces. Since the beam is in equilibrium, the sum of all vertical forces must be equal to zero, and the sum of all horizontal forces must also be equal to zero.
Step 5: Solve the equations to find the tension force and the compression force on the beam. The sum of vertical forces equation gives us the equation: Tension - Vertical component of weight force = 0. We can substitute the values we know (weight of the beam = mass of the beam times acceleration due to gravity) to find the tension force. The sum of horizontal forces equation gives us the equation: Horizontal component of weight force = 0. Therefore, there is no compression force acting on the beam.
Step 6: Solve for the tension force. Use the equation: Tension - Vertical component of weight force = 0. Rearrange the equation to solve for the tension force.
Let's calculate the tension force and the compression force in the beam using the given information:
Given:
Length of the beam (B) = 3 m
Angle between the beam and string = 30 degrees
Step 1: Draw a diagram with the beam (B) and the string (S) attached to the wall.
Step 2: Identify the forces:
- Tension force in the string (T)
- Vertical component of the weight force (Wv)
- Horizontal component of the weight force (Wh)
Step 3: Resolve the weight force:
Weight force (W) = mass of the beam (m) * acceleration due to gravity (g)
Since the mass is negligible and the sky weight holds the beam horizontally, we assume the horizontal component to be equal in magnitude but opposite in direction to the tension force.
Wh = T
Step 4: Set up equilibrium equations:
Sum of vertical forces: T - Wv = 0
Sum of horizontal forces: Wh = T
Step 5: Solve the equations:
Vertical component of weight force (Wv) = W * sin(angle between B and S)
Horizontal component of weight force (Wh) = W * cos(angle between B and S) = T (from step 3)
Sum of vertical forces equation: T - W * sin(angle between B and S) = 0
Tension force equation: T = W * cos(angle between B and S)
Step 6: Solve for the tension force:
Substitute W = m * g:
T = (m * g) * cos(angle between B and S)
Since the mass of the beam is not given, we cannot calculate the exact value of the tension force and the compression force without additional information. However, using the above equations and the given information, you can substitute the appropriate values to calculate the tension force and the compression force.
To find the tension in the string, we need to analyze the forces acting on the beam.
Let's consider the forces acting on the beam:
1. Tension in the string: This acts vertically upwards.
2. Weight of the beam: This acts vertically downwards.
3. Compression force: This acts horizontally towards the wall.
First, let's calculate the weight of the beam. The weight of an object is given by the formula:
Weight = mass * gravity
Since the mass is negligible and the beam is held horizontally, the weight can be considered zero.
Therefore, the weight of the beam is 0 N.
Next, let's look at the forces acting vertically. Since the beam is in equilibrium (no vertical motion), the upward force (tension) must be equal to the downward force (weight).
So, the tension in the string is also 0 N.
Finally, let's calculate the compression force. The compression force can be found using trigonometry. We can decompose the applied force into its vertical and horizontal components.
The vertical component of the force is Tension * sin(angle) = 0 * sin(30°) = 0 N.
The horizontal component of the force is Tension * cos(angle) = 0 * cos(30°) = 0 N.
Therefore, the compression force on the beam is also 0 N.
So, the tension in the string and the compression force on the beam are both 0 N.
In summary, the tension in the string and the compression force on the beam are both 0 N due to the beam being held horizontally with no weight.