A bridge of lenght 79 m and mass 1.1 x10^5 kg is supported at each end. A truck fo mass 20900 kg is located 31 m from the left end. What is the force on the bridge at the left point of support?
let x = support at left end
let y = support at right end
now, to get the reaction force at the left support, we sum moments at the right end, so that y will not be included in our calculation, and we can directly solve for x,,
*recall that moment = (force)*(distance perpendicular to that force) or
M = r x F (in vectors)
we use right hand rule to get the direction of the moment
when moment is out of the page, it's (+) and if into the page, it's (-)
anyway, summing moments at right end:
Given:
w,truck = 20900 * 9.8 N downward
W,bridge = 1.1 x 10^5 * 9.8 downward
direction of x and y is upward (assumed)
M, right end = 0 (because in equilibrium)
(79-31)(20900*9.8) + (79/2)(1.1 x 10^5 * 9.8) - (79)x = 0
note:
*distance from right end to truck is 79-31, and the force acting at this point is W,truck
*the W,bridge is acting on the center/middle of the bridge assuming uniform composition, thus the distance from right end to weight of bridge is 79/2 m
*the distance from right end to left end id 79, or simply the length of the bridge
solving,
x = 663447.6 N
since we got a positive answer, this means that the assumed direction is correct, thus
reaction at left end = 663447.6 N upward
hope this helps~ :)
To find the force on the bridge at the left point of support, we need to analyze the forces acting on the truck and the bridge.
1. Calculate the weight of the truck:
Weight of the truck = mass of the truck x acceleration due to gravity
Weight of the truck = 20900 kg x 9.8 m/s^2
Weight of the truck = 204620 N
2. Calculate the weight of the bridge:
Weight of the bridge = mass of the bridge x acceleration due to gravity
Weight of the bridge = 1.1 x 10^5 kg x 9.8 m/s^2
Weight of the bridge = 1078000 N
3. Calculate the distance between the left support and the truck:
Distance between the left support and the truck = 31 m
4. Calculate the weight of the bridge on the left side of the support:
Weight of the bridge on the left side of the support = (length of the bridge - distance between the left support and the truck) / length of the bridge x weight of the bridge
Weight of the bridge on the left side of the support = (79 m - 31 m) / 79 m x 1078000 N
Weight of the bridge on the left side of the support = 48 / 79 x 1078000 N
Weight of the bridge on the left side of the support = 652405.06 N
5. Calculate the force on the bridge at the left point of support:
Force on the bridge at the left point of support = weight of the truck + weight of the bridge on the left side of the support
Force on the bridge at the left point of support = 204620 N + 652405.06 N
Force on the bridge at the left point of support = 857025.06 N
Therefore, the force on the bridge at the left point of support is approximately 857025.06 Newtons.
To find the force on the bridge at the left point of support, we need to calculate the total force exerted on the bridge by the truck and the weight of the bridge itself.
Let's break down the problem into two parts:
1. Force exerted by the truck on the bridge:
The force exerted by the truck can be calculated using Newton's second law, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Since the truck is not accelerating, the force exerted by the truck is equal to its weight (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the force exerted by the truck is:
Force_truck = mass_truck * g
2. Weight of the bridge:
The weight of an object is equal to its mass multiplied by the acceleration due to gravity. Hence, the weight of the bridge is:
Weight_bridge = mass_bridge * g
Now, let's calculate the forces:
Given:
- Mass of the truck (m_truck) = 20900 kg
- Mass of the bridge (m_bridge) = 1.1 x 10^5 kg
- Length of the bridge (L) = 79 m
- Distance of the truck from the left end of the bridge (d_truck) = 31 m
- Acceleration due to gravity (g) ≈ 9.8 m/s^2
1. Force exerted by the truck:
Force_truck = m_truck * g
= 20900 kg * 9.8 m/s^2
2. Weight of the bridge:
Weight_bridge = m_bridge * g
= 1.1 x 10^5 kg * 9.8 m/s^2
Now, the total force exerted on the bridge at the left point of support is the sum of the force exerted by the truck and the weight of the bridge:
Total Force = Force_truck + Weight_bridge
You can compute the answer by substituting the given values into the equations and evaluating the expressions.