PHYSICS HIGH SCHOOL

The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d, and inversely as the length, l. A wooden beam 3in. wide, 6in. deep, and 11ft long holds up 1213lb. What load would a beam 6in. wide, 3in. deep and 12ft long of the same material support? (Round off your answer to the nearest pound.)

Answers

Answer 1
Answer:

Answer:

L' = 555.95 lb

Explanation:

Analyzing the given conditions in the question, we get

The safe load, L is directly proportional to width (w) and square of depth (d²)

 also,

L is inversely proportional length (l) i.e L = k/l

combining the above conditions, we get an equation as:

 L = k(wd²/l)

 now, for the first case we have been given

w = 3 in

d = 6 in

l = 11 ft

L = 1213 lbs

 thus,

1213 lb = k ((3 × 6²)/11)

or

k = 123.54 lbs/(ft.in³)  

Now,

Using the calculated value of k to calculate the value of L in the second case  

in the second case, we have

w = 6 in

d =3 in

l = 12 ft

Final Safe load L' =  123.54 × (6 × 3²/12)

or

L' = 555.95 lb
Answer 2
Answer:

Final answer:

The load that a beam of the given dimensions can support is derived using a joint variation formula. The constant of variaiton is found using the given beam's characteristics, and then applied on the second beam's measurements to find its load. The result is approximately 2025 pounds.

Explanation:

The question is related to joint variation and its principles in mathematics. First, it's necessary to define the equation of the joint variation:
L = k*(w*d^2)/l
where L is the load, w is the width, d is the depth, l is the length, and k is the constant of proportionality. From the information given in the question, we can derive that k equals to 1213 * 11 / (3 * 6^2), which is approximately 135. Then, we substitue the values of the second beam into the equation, w = 6, d = 3, l = 12 and k = 135, to get the load L for the second beam, which equates to about 2025 pounds.

Learn more about Joint Variation here:

brainly.com/question/33421771

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