Consider a train that rounds a curve with a radius of 574 m at a speed of 160 km/h. Calculate the friction force on the passenger if the train tilts at an angle of 8.0∘ toward the center of the curve.
To calculate the friction force on the passenger, we will use the concept of centripetal force.
The centripetal force is the force that keeps an object moving in a circular path and is directed toward the center of the curve. In this case, the friction force on the passenger will act as the centripetal force.
The formula for centripetal force is given by:
F = (m * v^2)/r
Where:
F is the centripetal force,
m is the mass of the object,
v is the velocity of the object,
r is the radius of the curve.
First, let's convert the speed from km/h to m/s:
160 km/h = 160 * (1000/3600) m/s = 44.44 m/s (rounded to two decimal places).
Now, let's convert the angle from degrees to radians:
8.0° = 8.0 * π/180 radians ≈ 0.14 radians (rounded to two decimal places).
Next, we need the mass of the passenger. Since it is not given, we will assume it to be 70 kg.
Now we can calculate the friction force on the passenger using the formula:
F = (m * v^2)/r
F = (70 * (44.44)^2) / 574
F ≈ 2839.54 N (rounded to two decimal places).
Therefore, the friction force on the passenger is approximately 2839.54 Newtons.