Question

load on crane 1 (b divided by (a + b) × load weight)
load on crane 2 (a divided by (a + b) × load weight)
load weight equals 375,000 pounds, a = 12 feet, b = 30 feet
capacity of crane 1 is 300,000 pounds
capacity of crane 2 is 275,000 pounds
note: figure not to scale

1. referring to the figure provided, determine the share of load weight which will be carried by each crane applying the following formula?

a. crane 1 = 107,143 lb, crane 2 = 267,857 lb
b. crane 1 = 164,286 lb, crane 2 = 410,744 lb
c. crane 1 = 267,857 lb, crane 2 = 107,143 lb
d. crane 1 = 410,714 lb, crane 2 = 164,286 lb

Explanation:

Step1: Calculate load on Crane 1

The formula for load on Crane 1 is $\frac{B}{A + B} \times \text{load weight}$. Given $B = 30$ feet, $A = 12$ feet, and load weight $= 375000$ pounds. First, calculate $A + B = 12 + 30 = 42$ feet. Then, the load on Crane 1 is $\frac{30}{42} \times 375000$. Simplify $\frac{30}{42}=\frac{5}{7}$, so $\frac{5}{7} \times 375000 \approx 267857$ pounds.

Step2: Calculate load on Crane 2

The formula for load on Crane 2 is $\frac{A}{A + B} \times \text{load weight}$. Using $A = 12$ feet, $A + B = 42$ feet, and load weight $= 375000$ pounds. So, $\frac{12}{42} \times 375000$. Simplify $\frac{12}{42}=\frac{2}{7}$, so $\frac{2}{7} \times 375000 \approx 107143$ pounds. Wait, no, wait: Wait, Crane 1's formula is (B/(A+B))×load weight, Crane 2's is (A/(A+B))×load weight. Wait, in the options, option c is Crane 1 = 267,857 lb, Crane 2 = 107,143 lb. Let's recalculate:

Crane 1: (30/(12+30))×375000 = (30/42)×375000 = (5/7)×375000 ≈ 267857.14 ≈ 267857 lb.

Crane 2: (12/(12+30))×375000 = (12/42)×375000 = (2/7)×375000 ≈ 107142.86 ≈ 107143 lb. So that's option c.

Answer:

c. Crane 1 = 267,857 lb, crane 2 = 107,143 lb