Examkin

Question

Difficulty: EasyLoad Distribution and Balancing

A 120120-pound crate rests on a sturdy 1212-foot plank spanning two sawhorses placed at opposite ends. The center of the crate is located 33 feet from the left sawhorse. Assuming the weight of the plank is negligible, what is the downward force, in pounds, exerted by the crate on the left sawhorse?

Answer: 90 pounds

Answer

The downward force exerted on the left sawhorse is 9090 pounds.
Because the crate is positioned 33 feet from the left sawhorse and 99 feet from the right sawhorse on a 1212-foot span, the left sawhorse must support 912\frac{9}{12} (or 75%75\%) of the crate's weight. Multiplying 120120 pounds by 0.750.75 yields exactly 9090 pounds.

Step-by-Step Solution

1
Calculate the distance from the crate to the right sawhorse.
12−3=912 - 3 = 9 feet.
The weight supported by one end of a beam is proportional to the distance from the load to the opposite end.
2
Determine the fraction of the total weight carried by the left sawhorse.
912\frac{9}{12}, which simplifies to 34\frac{3}{4} or 0.750.75.
This fraction represents the ratio of the opposite distance to the total span, dictating how much load is distributed to the left support.
3
Calculate the downward force on the left sawhorse.
120×0.75=90120 \times 0.75 = 90 pounds.
Multiplying the total crate weight by the calculated proportion gives the specific load carried by that support.

Key Concept

Load Distribution and Balancing
Estimated Time:45s
Rate this question

Topics

Load Distribution and Balancing

More questions from this topic