Friction problem with banked curve given static friction coefficient

In summary: First, solve for the Vertical force: Fv=ma. Second, solve for the Horizontal force: Fh=ft. Vertical force: Fv=maFh=ftAcceleration: 0
  • #1
zenith12
2
0

Homework Statement



What is the maximum speed with which a 1200 rubber-tired car can take around a banked curve with radius of 80.0 meters an angle of 19.0 degrees? (static friction coefficient is 1.0)


Homework Equations


Fs=mu*F(normal)
F(netxdirection)/m=acceleration
acceleration=velocity2/radius


The Attempt at a Solution


I tried answering this problem several times and I failed at each; although I swear my first answer was correct (31.6 m/s). My professor's answer was 40.1 m/s and I have no idea how he got that.

Please help...
 
Physics news on Phys.org
  • #2
Show how you solved it. What are your vertical and horizontal force equations?
 
  • #3
Hey...sorry for being so short. I was in a hurry to just get the question asked. I spent all day on homework and no time to fully explain.

Here are my notes on this problem:

Known:
incline angle=19.0 degrees
Radius of turn=80.0 m
Mass of car=1200 kg
mu(s) tire on cement road=1.0

Forces:
Normal
Weight
Friction

Find:
Max velocity without slipping on cement

Steps:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
2. Enter Normal in Friction equation (F=mu*N) to get Friction force.
3. Enter Friction force in F(netx)=ma for x-axis to solve for acceleration in the x direction which is also the radial/centripetal direction btw.
4. Use a=v^2/r to find the velocity.

Maybe this velocity is not the maximum? Am I missing something conceptual?
 
  • #4
zenith12 said:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
Careful! The acceleration is horizontal, so you cannot say that the acceleration is zero normal to the incline.

Instead, analyze vertical and horizontal force components. Set up two equations and solve them together.
 

1. What is a banked curve?

A banked curve is a curved track or road that is inclined at an angle, designed to allow vehicles to safely navigate the curve at high speeds.

2. How does friction affect a banked curve?

Friction plays a crucial role in allowing a vehicle to safely navigate a banked curve. It helps to keep the vehicle from sliding off the track or road and allows it to maintain its speed and direction.

3. What is the purpose of the static friction coefficient in this problem?

The static friction coefficient is a measure of the amount of friction between two surfaces in contact when there is no relative motion between them. In the context of a banked curve, it is used to determine the maximum speed at which a vehicle can safely navigate the curve without slipping off the track or road.

4. How can the static friction coefficient be calculated?

The static friction coefficient can be calculated by dividing the maximum frictional force that can be exerted between two surfaces by the normal force pressing the two surfaces together. This value is dependent on the nature of the two surfaces in contact and can be experimentally determined.

5. What factors can affect the value of the static friction coefficient in a real-world scenario?

The value of the static friction coefficient can be affected by factors such as the nature and condition of the surfaces in contact, the weight and speed of the vehicle, and any external forces acting on the vehicle (e.g. wind). It is important to regularly monitor and adjust the static friction coefficient to ensure safe navigation of the banked curve.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
17
Views
697
  • Introductory Physics Homework Help
Replies
3
Views
6K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
782
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
Back
Top