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

1. referring to the figure provided, determine the share of load weight which will be 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, $\frac{30}{42} \times 375000 = \frac{30 \times 375000}{42} \approx 267857$ 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, $\frac{12}{42} \times 375000 = \frac{12 \times 375000}{42} \approx 107143$ pounds.

Answer:

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