a 5000lb truck is 20.0ft from one end of a 50.0ft bridge. a 4000lb car is 40.0ft from the same end. how much weight must each end of the bridge support?(neglect the weight of the bridge.)
To determine how much weight must each end of the bridge support, we need to consider the weight distribution based on the distances from the ends.
Let's denote the weight that each end of the bridge must support as W1 and W2.
Given information:
- Weight of the truck (Wtruck) = 5000 lb
- Distance of the truck from one end (dtruck) = 20.0 ft
- Weight of the car (Wcar) = 4000 lb
- Distance of the car from the same end (dcar) = 40.0 ft
First, let's determine the total weight on the bridge.
Total weight on the bridge = Weight of the truck + Weight of the car
= Wtruck + Wcar
= 5000 lb + 4000 lb
= 9000 lb
Now, let's calculate the weight distribution:
The weight distribution is directly proportional to the distances from each end.
W1/W2 = (d2/d1)
Where:
W1 = Weight on one end of the bridge
W2 = Weight on the other end of the bridge
d1 = Distance of the truck from one end
d2 = Distance of the car from the same end
Substituting the given distances:
W1/W2 = (dcar/dtruck)
W1/W2 = 40.0 ft / 20.0 ft
W1/W2 = 2
Now, we can solve for W1 and W2.
W1 + W2 = Total weight on the bridge
W1 + W2 = 9000 lb
Using the weight distribution equation, we have W1 = 2W2. Substituting this into the previous equation:
2W2 + W2 = 9000 lb
3W2 = 9000 lb
W2 = 9000 lb / 3
W2 = 3000 lb
Now, we can find W1:
W1 = 2W2
W1 = 2 * 3000 lb
W1 = 6000 lb
Therefore, each end of the bridge must support 6000 lb and 3000 lb of weight.