What is Banked curve: Definition and 110 Discussions
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.
This isn't really a question per se, but it recently just 'clicked' for me and I would like to share what made that do so.
There are dozens of threads answering this question, but in my opinion most (but not all; there are some good threads on this forum, I just want to show how I came to...
If there is a car resting on a banked curve with angle theta, velocity v = 0, but N (normal)*sin(theta) > 0. So N*sin(theta) =/= (m*v^2)/r with v = 0. But my physics textbook just defined N*sin(theta) = (m*v^2)/r in banked curve. What is going on here?
Here's a FBD I made for this question.
From the diagram, I obtained that ##-W + N \cos\theta - f_s \sin\theta = 0##. And ##N\sin\theta + f_s \cos\theta = ma = \frac{mv^2}{R} \leq N\sin\theta + f_s^{\max} \cos\theta = \frac{mv_{\max}^2}{ R}##. Solving these equations, and using the angle...
First I figured out the normal force being exerted on the car using the equation above.
Cos(40°)*(1050*9.8) = 7883N
Next, I tried to find out the horizontal component of the normal force by doing:
Cos(50) * 7883 = 5067N
I figured out the angle by using certain geometrical properties.
Next, I...
Ok so I think that the equation for centripetal force is the mv^2/r and this SHOULD equal the horizontal component of the normal force on the car. Vertical component of normal force and gravity would cancel out. However, when I input the numbers into the equations I don't get equivalent values...
Homework Statement
If a curve with a tedious of 80m is perfectly banked for a car traveling 70km/h, what must be the coefficient of static friction for a car not to skid when traveling at 90 km/h ?
Homework Equations
Newton’s second law
F=ma
The Attempt at a Solution
To find the angle of the...
Homework Statement
A car giving a turn on a curve with 88m of radius, traveling at a speed of 95km/h, the curve is perfectly banked for a car traveling at 75 km/h, meaning that the curve has an angle θ of 26.7º.
Homework Equations
μ = ?
r = 88m
v = 26.38 m/s
θ = 26.7º
Ff = μ · g · m
Fc = m...
I understand why when deriving the formulas for cars on banked curves, the net force in the Y direction is zero. However, when I google how to derive them, people say that there is a net force greater than zero in the X direction. This is not what my professor says in his explanations however...
Homework Statement
13.49 The flatbed railway car travels at the constant speed of 80 km/h around a curve
of radius 55m and the bank angle 15deg. Determine the smallest static coefficient of friction between the crate and the car that would prevent the crate of mass M from sliding.
Homework...
Why during a banked curve is the horizontal component of the normal force considered as the net force and the centripetal force? The horizontal component of Normal force, N·sinθ, is not even ponting towards the centre of the curvature.
Homework Statement
A car is making a turn on a wet highway ramp. The coefficient of static friction between the tires and the road is 0.25. Determine the maximum speed at which the car can safely negotiate a turn of radius 200m with a banking angle of 20 degrees.
radius= 200m
μs=0.25...
Hello Forum,
In the situation of a car banking a curve there are two forces: weight W and the normal force N. Theta is the banking angle between the road and the horizontal.
The vector addition between W and N gives a net force F_net that is directed toward the center. That F_net is the...
Homework Statement
A car traveling 10 m/s is moving along a track banked at 5 degrees. The tire-road friction coefficient is .3 What is the minimum radius it can travel without slipping?
v0= 10 m/s
Bank Angle Θ = 5°
μ=0.3
Note I am working through prep material for the exam. The solution...
Hi all,
I was wondering if anyone could help me with calculating the angle of lean on a motorbike on a banked curve (with friction). If possible proofs would be very useful.
Thanks
Lee
A problem states " For a banked curve, ignoring friction, prove that tan θ = ν^2/rg". I tried to prove but I thought that as the normal force is at right angle to track then how could be the component of normal force provide the centripetal force as my book is saying. Please someone help. I...
Relative equations:
F = ma
a = v^2/r
Fcent = mv^2/r
ωf^2 – ωi^2 = 2αs
s = θr
ω = v/r
Problem statement and work so far are all included:
(I am having trouble with 5 and no clue how to start on 7-9)
You are designing a roadway for a local business, to include a circular exit ramp from the...
So I'm having a hard time understanding baked turns involving roads. Mainly I'm confused on how to derive the friction force into the x and y components and why it turns be like so. I also am confused about when i encounter a problem that involves friction in banked turns like in the picture...
I'm confused trying to understand the previous steps that lead to the formula for the angle of an ideally banked curve. In absence of friction, this is the angle where the Centripetal Force is provided by the horizontal component of the Normal Force.
I understand that the Normal Force is...
Homework Statement
A civil engineer is asked to design a curved
section of roadway that meets the following
conditions:
With ice on the road, when the coefficient of
static friction between the road and rubber is 0.12, a car at rest must not slide into the ditch
and a car traveling less than 70...
Homework Statement
A town wants to build a banked curve to join to large roads. The maximum speed they would like cars travel on this curve is 51m/s. The angle of the banked curve is to be 19o and the radius is to be 1.8x102 m.
a) What does the coefficient of static friction need to be...
Homework Statement
A curve with a 140m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction between tires and road needed to prevent skidding?
Homework Equations
F_fr =...
Homework Statement
Designing an on ramp for the 401 the engineer wants cars to be able to make the turn with a radius of 50 m while traveling 40km/hr in conditions with no friction. What angle must he bank the curve at to make this possible? Homework Equations
FR = (m)(aR)
FR = (m)(v2)/(r)The...
Homework Statement
A banked curve has been designed so that it is safest for a vehicle going 70 mph. The topography of the land restricts the radius of the road to 300m. Assume mu(static friction) is 0.80 and mu(kinetic friction) is 0.60.
A 5512 lb vehicle travels with a speed of 60 mph on...
Homework Statement
A curve of radius 67 m is banked for a design speed of 95 km/h. If the coefficient of
static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the
curve?
Homework Equations
I drew this freebody diagram.
The Attempt at a...
This is my first thread on the forum. I'm really glad to have found this wonderful resource. I have a lot of intuition in mathematics and one of my dreams has been to have the same level of intuition in physics. With your help I hope I can achieve that.
I was reading an example in Physics...
Hey all,
I'm in the process of writing a report concerning the physics of rollercoasters going around banked curves. With the rollercoaster I'm focussing on, the velocity of the car is always greater than the designed velocity of curves meaning there is a friction force parallel to the bank...
hello good morning. Let look at the two diagram.
(back view)
In STATIC, a car is remauning static at a bank curve and its force diagram is as follows. for this case, the normal force is smaller than the weight of the car and friction exists in the directiin perpendicular to car.
In MOTION...
Homework Statement
A curve of radius 60 m is banked for a design speed of 100km/h. If the coefficient of static friction is 0.30, at what range of speeds can a car safely make the turn.
Homework Equations
Fun=ma
Ff=μsFn
Fc=mV2/r
The Attempt at a Solution
So, when it is...
how can rcosθ in a banked road be equal to mg; since r is equal to normal reaction which is equal to mgcosθ. rcos is even smaller than r.
so
mg>mgcosθ
mgcosθ=r
r>rcosθ
so
mg>rcosθ
then how can mg=rcos when banking in curved road?
Homework Statement
A certain curve on a freeway has a radius of 200m and is banked at an angle of 25°. A 200-kg car moves around the curve at constant speed.
1. If the speed of the car is 35m/s, what friction force is needed to keep the car moving in a circle?
2. If the speed of the car...
Homework Statement
A 1000kg car travels around a frictionless banked curve having a radius of 80m. If the banking is 20 degrees to the horizontal, at which specific speed must the car travel to maintain a constant radius?
Homework Equations
Fc = mv^2/r
Fg(perp.) = mgcos(20)
The...
If the wheels and tires of a car are rolling without slipping or sliding when turning, the bottom of the tire is rest against the road at each instant, so the force of friction is the static friction. Essentially if you are moving around a banked curve and the car is not skidding, then friction...
Homework Statement
A 1200kg car rounds a dry curve (μ= .6)with a radius of 67 m banked at an angle of 12°. If the car is traveling @ 95 km/hr (26.4 m/s), will a friction force be required? If so how much and in what direction?
Homework Equations
Fn = mg cos 12°
ƩFn sin 12° = m (v^2/r)...
ƩHomework Statement
A car of mass 2,000 kg is moving round a curve on a
banked track (see diagram-We were actually only given the top picture "a" and not the bottom one, but both are relevant) at a constant speed. The
coefficient of static friction between the car's tires and
the track is...
Homework Statement
A 1200 kg car rounds a banked curve of radius 70 m. If the banked angle is 12° and the car is traveling at 90 km/h, show that friction is necessary in order for the car to safely make the turn.
Homework Equations
Force of gravity: Fg=m*g
to calculate the normal...
Homework Statement
At what angle should the roadway on a curve with a 50m radius be banked to allow cars to make the curve at 12 m/s even if friction is 0?
Homework Equations
The Attempt at a Solution
All of the centripetal acceleration comes from normal force from the road on...
If a curve with a radius of 89.0m is perfectly banked for a car traveling 71.0km/hr, what is the minimum coefficient of static friction for a car not to skid when traveling at 91.8km/hr?
I figured out theta = 24. 03degs from the equations F(normal)*cos(theta) = mg and F(normal)*sin(theta) =...
Homework Statement
a racecourse is designed with curves with a radius of 200m and a 10degree banking. What is the maximum speed a car can negotiate the curve without friction?
Homework Equations
Newtons 3 laws
The Attempt at a Solution
tanTheta = v^2/gR
tan10 = v^2/(9.8 * 200m)
v...
Homework Statement
A 1200 kg car travels around a curve banked at 42.5 degrees in a circular path of radius = 150m, but the ramp is only 55m long. The force of friction on the car is 9000N, calculate the speed of the car.
So:
radius = 150 m
θ (angle the incline makes with the...
Homework Statement
At what angle should the roadway on a curve with a 50 m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is frictionless?
a. 0°
b. 12.2°
c. 17.1°
d. 35.0°
e. 73.2°Homework Equations
β=arctan(v^2/r*g) The Attempt at a Solution
im using...
Homework Statement
A turn in the road with a radius of 30m is banked at an angle of 40 degrees. If \mu=.75, what is the minimum and max speed a 1200 kg car can travel without sliding off the turn.
Homework Equations
F=ma, Mv^2/R, Fw = mg
The Attempt at a Solution
Alright, so...
I am stumped on this problem. If anyone can help it would be greatly appreciated.
A plane is approaching an airport in a traffic holding pattern. While awaiting its clearence to land, the plane traverses a horizontal circle of radius 2520 meters at constant speed, Each complete turn of the...
Banked Curve "perfectly banked"
Homework Statement
if a curve with a radius of 88. is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not to skid when traveling 95km/h?
Homework Equations
ƩF=ma and a=v^2/r and Ff=μFnThe Attempt at a...
Hey guys I know this is probably easy for most of you but I need help with a banked curve problem. The problem is as follows "Suppose you ride a bicycle in a 20-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle (normal force plus frictional...
I am researching for a sci-fi screenplay that I am writing for fun. To keep bone density from losing the estimated 1.5% per month on Mars I want to simulate Earth gravity by having the colonists live aboard condominiums that are fitted with a rail car suspension and travel in a perfect circle in...
If a car can negotiate a curve of radius 200 m at 30 m=s without any frictional force being
required, what is the banking angle
r = 200 m
v = 30 m/s
tanΘ = v2/r
Θ = tan-1(v2/r]
Θ = tan-1(302/200]
Θ =77.47 degrees
I thought this problem was a simple one, but the answer that is...
Homework Statement
A train on the planet surface of Mars is traveling along a banked track shaped as large circle with a radius of 500m.
Q. Assuming Mars gravity is 3.8m/s^{2} what Velocity v must the Martian train travel to simulate a total artificial gravity equal to Earth's...
Homework Statement
I;m trying to prove if this guy is guilty or not, after crashing on a curve. This is mulitpart, but i will only do one at a time to not confuse. The first thing I have to do is find the coefficient of static friction. I have a drag sled test, which required a force of 42...
Homework Statement
A car with mass 1200kg rounds a curve banked at 18 degrees. The radius of the curve is 130 m.
Find the speed of the car if the frictional force between the tires and the road is 3.5 x 10^3 down the banked curve.
Homework Equations
ac = v2/r
The Attempt at a Solution...