Consider a train that rounds a curve with a radius of 570m at a speed of 160 km/h (approximately 100 mi/h)Calculate the friction force needed on a train passenger of mass 75kg if the track is not banked and the train does not tilt.
force=mv^2 / RADIUS
Change velocity to m/sec
Well, well, well, look who's on track with a physics question! Alright, let's chug along and see what we can do.
To calculate the friction force needed, we need to keep in mind that the track isn't banked and the train doesn't tilt. So, the only thing keeping our passenger from flying off like a circus act is the friction force. Good thing it's not a clown car!
First, let's convert that speed into good ol' meters per second. 160 km/h equals 44.4 m/s. So, our daring passenger is zooming around that curve at 44.4 m/s.
Now, we need to find the acceleration of our passenger. And here comes the formula: acceleration (a) equals velocity squared (v^2) divided by the radius of the curve (R).
Plugging in the values we have, the acceleration (a) is 44.4 m/s squared divided by 570m. Let's crunch those numbers. *Calculating sounds* And we get... a = 0.349 m/s².
Since the acceleration of our passenger is towards the center of the curve, the friction force acting on them is in the opposite direction, trying to keep them from flying out of their seat. Ah, the joys of physics!
Now, we just need to find that friction force (F). Using good ol' Newton's second law, F = mass (m) times acceleration (a).
Plugging in the mass of our passenger, 75 kg, and the acceleration we found earlier, 0.349 m/s², let's do the math! *Tap-tap-tap* And we get... F = 26.175 N (approximately).
So, drumroll, please! The friction force needed to keep our passenger comfortably seated through that curve is approximately 26.175 Newtons. Just enough to keep them from doing acrobatics in the aisle. Phew!
Remember, safety and physics go hand in hand. Stay seated, laugh a little, and enjoy the ride!
To calculate the friction force needed on a train passenger, we first need to calculate the acceleration of the train as it rounds the curve. In this case, since the track is not banked and the train does not tilt, the friction force provides the centripetal force needed for the train to move in a curved path.
We can use the centripetal acceleration formula to find the acceleration:
a = v^2 / r
Where:
a = acceleration
v = velocity (speed of the train)
r = radius of the curve
Converting the given speed from km/h to m/s, we have:
v = 160 km/h * (1000 m/km) / (3600 s/h)
= 44.4 m/s
Substituting the values into the formula:
a = (44.4 m/s)^2 / 570 m
= 3.47 m/s^2
Now, we can calculate the friction force using Newton's second law of motion:
F = m * a
Where:
F = force (friction force)
m = mass of the passenger
a = acceleration
Substituting the values:
F = 75 kg * 3.47 m/s^2
= 260.25 N
Therefore, the friction force needed on the train passenger of mass 75 kg is approximately 260.25 Newtons.
To calculate the friction force needed on a train passenger, we need to consider the centripetal force acting on the passenger as the train rounds the curve. The centripetal force is provided by the static friction force between the passenger and the seat.
Here's the step-by-step process to calculate the friction force:
1. Convert the speed of the train from km/h to m/s:
Speed = 160 km/h = (160 * 1000) m/3600 s = 44.44 m/s
2. Calculate the acceleration of the train using the formula:
Acceleration = (Speed^2) / Radius
Acceleration = (44.44 m/s)^2 / 570 m ≈ 3.468 m/s^2
3. Apply Newton's second law of motion to find the force:
Force = Mass × Acceleration
Force = 75 kg × 3.468 m/s^2 ≈ 260.1 N
Therefore, the friction force needed on the train passenger of mass 75 kg when the track is not banked and the train does not tilt is approximately 260.1 Newtons.