Examkin

Question

Difficulty: EasyLoad Distribution and Balancing

A footbridge spans a 2020-foot wide creek, resting on a concrete pillar at each end (Left Pillar and Right Pillar). A person weighing 160160 pounds stands on the bridge, exactly 55 feet from the Right Pillar. If we ignore the weight of the bridge itself, how many pounds of the person's weight are supported by the Left Pillar?

Answer: 40 pounds

Answer

40
The weight supported by the Left Pillar is inversely proportional to the load's distance from it. Since the person is 1515 feet from the Left Pillar and 55 feet from the Right Pillar on a 2020-foot bridge, they are 33 times closer to the Right Pillar. Therefore, the Right Pillar carries 3/43/4 of the weight (120120 lbs) and the Left Pillar carries 1/41/4 of the weight (4040 lbs).

Step-by-Step Solution

1
Determine the relevant distances along the bridge.
Total span = 2020 ft. Distance to Right Pillar = 55 ft. Distance to Left Pillar = 1515 ft.
To calculate the load on one support, we need the total distance and the distance to the opposite support.
2
Set up the load distribution calculation for the Left Pillar.
Load on Left Pillar = Total Weight ×\times (Distance to Right Pillar / Total Span)
The proportion of weight supported by one end of a beam is equal to the distance from the load to the opposite end, divided by the total length.
3
Calculate the supported weight using the values.
160×(5/20)=160×(1/4)=40160 \times (5 / 20) = 160 \times (1 / 4) = 40 pounds.
Solving the equation gives the exact weight carried by the left support.

Key Concept

Load Distribution and Balancing

Alternative Method

You can also use the concept of torque (moments) in static equilibrium. Taking the Right Pillar as the pivot point: (Force of Left Pillar ×\times 2020 ft) = (160160 lbs ×\times 55 ft). Therefore, 20×Fleft=80020 \times F_{left} = 800, which means Fleft=40F_{left} = 40 lbs.
Estimated Time:45s
Rate this question

Topics

Load Distribution and Balancing

More questions from this topic