The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L.
a. Write an equation that expresses this prportionality
b. Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb.
c. If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?
So far, I've got the equation. It's M=k^2wh^2/L. I need help working out the problem.
M=k*wh^2/L
I don't know why you squared k, the constant.
4800=K*4*36*12 note units in*in^2*ft
k=100/36
M=100/36*3*100*10=100,000/36=?
the weight that a beam can support varies inversly as the length,suppose a 12 foot beam can support 12000 pounds how many pounds can a 15 foot beam support
The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam foot wide, foot high, and 10 feet long can support 12 tons find how much a similar beam can support if the beam is foot wide, foot high, and 16 feet long.
To solve this problem, we will use the given information and the formula you have correctly identified, which is:
M = k^2 * (w * h)^2 / L
a. First, we need to write an equation that expresses the proportionality. The proportionality statement tells us that maximum weight M is jointly proportional to width w, the square of height h, and inversely proportional to length L. We can write this as:
M ∝ (w * h^2) / L
Using the proportionality constant k, we can then write the equation as:
M = k * (w * h^2) / L
b. To determine the constant of proportionality (k), we can use the given information about a beam that is 4 inches wide, 6 inches high, and 12 feet long, supporting a weight of 4800 pounds. We can substitute these values into the equation and solve for k:
4800 = k * (4 * 6^2) / 12
First, simplify the equation:
4800 = 24 * k
Now, solve for k:
k = 4800 / 24
k = 200
So, the constant of proportionality in this case is 200.
c. For the 10-ft beam that is 3 inches wide and 10 inches high, we can use the proportionality equation and the value of k obtained in the previous step:
M = k * (w * h^2) / L
Substitute the given values:
M = 200 * (3 * 10^2) / 10
Simplify the equation:
M = 200 * 3 * 10
M = 6000
Therefore, the maximum weight the 10-ft beam can support is 6000 pounds.
In summary, the equation expressing the proportionality is M = k * (w * h^2) / L, with a constant of proportionality of k = 200. Using this equation, we found that the 10-ft beam can support a maximum weight of 6000 pounds.