Answer:
The tension in the steel beam is 14.72 Newtons.
Step-by-step explanation:
To calculate the tension in the steel beam when a car is hanging from it, you can use the principles of static equilibrium. In this situation, the gravitational force acting on the car must be balanced by the tension in the steel beam.
First, let's calculate the gravitational force acting on the car:
F_gravity = mass × gravity
Where:
Mass (m) = 1560 kg
Gravity (g) ≈ 9.81 m/s² (standard acceleration due to gravity)
F_gravity = 1560 kg × 9.81 m/s² ≈ 15306 N
Now, this gravitational force is balanced by the tension in the steel beam. Since the beam bends with an angle of 0.055°, we need to consider the vertical component of the tension force.
The vertical component of the tension (T_vertical) can be calculated using trigonometry (considering the angle θ):
T_vertical = T × sin(θ)
Where:
T_vertical is the vertical component of tension.
T is the tension in the beam.
θ is the angle in radians.
We need to convert the angle from degrees to radians:
θ = 0.055° × (π/180) ≈ 0.000959 radians
Now, we can calculate T_vertical:
T_vertical = 15306 N × sin(0.000959) ≈ 14.72 N
So, the tension in the steel beam is 14.72 Newtons.