Final answer:
The maximum load supported by a beam can be calculated using joint variation and inverse variation concepts.
Given the dimensions and load of the first beam, we can find the constant of variation and will get the maximum load supported by the new beam is 480 kg.
Step-by-step explanation:
To find the maximum load supported by the beam, we need to use the given information and apply the joint variation and inverse variation concepts.
The maximum load varies jointly as the width and the square of the height, and it is inversely proportional to the length between the supports.
Given:
- Length (l1) = 6 m
- Width (w1) = 0.1 m
- Height (h1) = 0.06 m
- Maximum load (m1) = 360 kg
Using the given values, we can set up the joint and inverse variation equation:
m1 = k * w1 * h1^2 / l1
Solving for k:
k = m1 * l1 / (w1 * h1^2)
Now we can find the maximum load for the new beam:
- Length (l2) = 16 m
- Width (w2) = 0.2 m
- Height (h2) = 0.08 m
Using the equation above with the new values, we can calculate the maximum load:
m2 = k * w2 * h2^2 / l2
Substituting the known values, we get:
m2 = (m1 * l1 / (w1 * h1^2)) * w2 * h2^2 / l2
Plug in the values and calculate:
m2 = (360 * 6 / (0.1 * 0.06^2)) * 0.2 * 0.08^2 / 16 = 480 kg
Therefore, the maximum load supported by the new beam is 480 kg.