A bridge is 200 m long. A car weighing 2.5 metric tons is 50 m from one end of the bridge and a trucj weighing 6 metric tons is 80 m from the other end. The bridge is uniformly paved and weighs 20 metric tons. How much force does the vertical support at each end exert?
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To find the force exerted by the vertical support at each end, we need to consider the weight of the vehicles and the bridge itself.
Let's break down the problem step by step:
1. Determine the weight of the car:
Given that the car weighs 2.5 metric tons, we need to convert it to kilograms since the SI unit for weight is kilograms.
1 metric ton = 1000 kilograms, so the weight of the car is 2.5 × 1000 = 2500 kilograms.
2. Determine the weight of the truck:
Similarly, the weight of the truck is 6 metric tons or 6 × 1000 = 6000 kilograms.
3. Determine the weight of the bridge:
The bridge itself weighs 20 metric tons, which equals 20 × 1000 = 20000 kilograms.
4. Calculate the forces at each end:
To determine the force exerted by the vertical support at each end, we need to consider the weight distribution. Assuming the bridge is symmetrically placed between the car and the truck, the distance between the car and the truck from the center of the bridge will be equal.
Let's call the distance between the support and the car "x" and the distance between the support and the truck "y". The sum of x and y will be half the length of the bridge, so x + y = 200/2 = 100 meters.
Now, we need to find the forces exerted by the vertical supports at each end.
Force exerted by the vertical support at the end of the car:
The weight of the car acts at a distance of 50 meters from the support. So, the force exerted by the support at the end of the car is (2500 kg) × (9.8 m/s^2) = 24500 Newtons.
Force exerted by the vertical support at the end of the truck:
The weight of the truck acts at a distance of 80 meters from the support. So, the force exerted by the support at the end of the truck is (6000 kg) × (9.8 m/s^2) = 58800 Newtons.
Therefore, the force exerted by the vertical support at each end is 24500 Newtons for the car end and 58800 Newtons for the truck end.