A bridge is supported at both ends (500m between supports). A Car (250 Kg) is at 100m from the left support. A truck (4000 Kg) is at 200m from the left support. Find the forces on the supports
1+1 = 2
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To find the forces on the supports of the bridge, we need to consider the weight of the car and the truck and their respective positions on the bridge.
Let's start by calculating the total weight of the car and the truck:
Weight of the car = mass of the car × acceleration due to gravity
= 250 kg × 9.8 m/s^2
= 2450 N
Weight of the truck = mass of the truck × acceleration due to gravity
= 4000 kg × 9.8 m/s^2
= 39200 N
Next, let's calculate the moments caused by the car and the truck.
Moment = weight × distance
Moment caused by the car = weight of the car × distance from the left support
= 2450 N × 100 m
= 245000 Nm
Moment caused by the truck = weight of the truck × distance from the left support
= 39200 N × 200 m
= 7840000 Nm
Now, let's find the forces on the supports.
Since the bridge is supported at both ends, the total downward force of the bridge must be equal to the sum of the weights of the car and the truck:
Total downward force = weight of the car + weight of the truck
= 2450 N + 39200 N
= 41650 N
The total upward force on the left support should balance the total downward force:
Total upward force on the left support = Total downward force
= 41650 N
Since the bridge is symmetrical, the total upward force on the right support should also be the same:
Total upward force on the right support = Total upward force on the left support
= 41650 N
Therefore, the forces on the supports of the bridge are both 41650 N.