A while crossing a bridge that is 3.6 km long, a truck weighing 9000 N is stalls 0.6 km from the left side of the bridge
Calculate the torque about the left support due to the truck
Wouldn't it depend on the weight of the bridge? OK, the bridge is massless.
about the left side: 9000*.6 is the torque due to the truck. Of course, the bridge weight matters, as does the right support holding half the bridge.
see that's where is confused me. It didn't give me anything for the weight of the bridge.
And I tried 9000*.6 and it's still saying i'm wrong.
This is kind of what the diagram looks like. O is the truck
F left
^
I
I ^ F right
I I
I_____O___________________I
I
I
I
V weight
torque on the left is: assume there is no support on the right side, and you are left with a wrench lever arm: distance from left: 600m x 9000N.
(clockwise)
To calculate the torque about the left support due to the truck, we first need to find the weight of the truck. We know that weight is equal to the mass multiplied by the acceleration due to gravity. Therefore, weight (W) = mass (m) * acceleration due to gravity (g).
Given that the weight of the truck is 9000 N, we can find the mass using the equation:
m = W / g
Assuming the acceleration due to gravity is 9.8 m/s^2, we can substitute the given values into the equation:
m = 9000 N / 9.8 m/s^2
m ≈ 918 kg (rounded to three decimal places)
Next, we need to calculate the distance of the truck from the left support in meters, as torque is dependent on the distance from the pivot point. The given distance is 0.6 km, which is equal to 0.6 * 1000 = 600 meters.
Now, we can calculate the torque (τ) about the left support using the formula:
τ = force (F) * distance (d)
Since torque is equal to the cross product of force and distance, we need to calculate the perpendicular component of the truck's weight acting on the bridge. This can be done using trigonometry. Considering the weight (force) acts vertically downwards, and only the vertical component contributes to the torque, we can use the following formula:
F_perpendicular = W * sin(θ)
In this case, the angle (θ) is 0 degrees since the force vector is vertical. Therefore, sin(θ) = sin(0°) = 0. In this scenario, the entire weight acts vertically downwards, so F_perpendicular = W.
Finally, we can calculate the torque:
τ = F_perpendicular * d
Substituting the value of F_perpendicular (which is equal to W), and the value of d (600 m), into the equation:
τ = 9000 N * 600 m
τ = 5,400,000 Nm
Therefore, the torque about the left support due to the truck is 5,400,000 Nm.