A 75.0 kN truck is parked in the middle of a 20.0 m long bridge. How much force must each end of the bridge exert to support the truck?
To determine the force required at each end of the bridge to support the truck, we can use the principle of equilibrium. According to this principle, the sum of the forces acting on an object at rest should result in a net force of zero.
In this case, we have a truck parked on a bridge, which means it is not moving. Therefore, the forces acting on the truck must be balanced.
We know that the weight of the truck is 75.0 kN (kilonewtons), which is equivalent to 75,000 newtons (since 1 kN = 1000 N). This weight is acting downward due to gravity.
Since the truck is not moving vertically, the forces acting upwards must balance the weight of the truck. The force exerted at each end of the bridge will share this weight equally.
Therefore, to find the force at each end of the bridge, we can divide the weight of the truck by 2 since there are two ends supporting it.
Let's calculate:
Force at each end = Weight of truck / 2
= (75,000 N) / 2
= 37,500 N
So, each end of the bridge must exert a force of 37,500 newtons to support the truck.