Show me - Car on a Banked Road

The applet Car on a Banked Road simulates the motion of a car as it rounds a corner.

Preamble

This applet can be used to illustrate the physics of traveling around a corner. Cases involving friction and a banked curve can be investigated.

This page is designed to get you started using the applet. The applet should be open. The step-by-step instructions on this page are to be done in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.

Contents

The applet Car on a Banked Road is intended to illustrate the subtle interplay between the forces of gravity, friction and the normal force for an object traveling in a circular path.

Forces and Free Body Diagrams

To start, press the Free Body Diagram button . The following menu will open:

Select all of the options. You should see a Fee Body Diagram drawn on the left side of the display panel. Since you have selected the "move FBDs" check box you can grab the FBD with the mouse and move it anywhere on the panel. You can tell this mode is working if a green circle appears as you move the cursor to the center of the force diagram.

To help see the FBD better you should select the "hide image mode" by pressing
You should see something like the following: Note that only the normal force and weight have non-zero magnitude. In order to produce a frictional force it will be necessary to adjust the input values. We will do that next.

Adjusting the Input Values and How this affects the FBD

Set the speed and coefficient of static friction to the values shown on the left. Note that the FBD changes as you do this. The FBD should now look like the following. Note that the force of friction is no longer zero and is also directed inward - toward the center of the turn. Try changing the speed or coefficient of friction and observe how the frictional force changes.

 

Now introduce an angle of 22.5 degrees and notice how the FBD changes:

  • both the normal force and frictional force vectors change in length
  • force components now appear in black
 

Next, reduce the speed of the car from 26.0 m/s to 8.3 m/s and observe the effect that this has on the size and direction of the frictional force vector. Experiment with various choices of speed, angle and coefficient of friction.

 

How to Get Quantitative Data from the Applet

To get quantitative data concerning magnitudes of forces and components press the button. The following dialogue opens:

The information presented gives the magnitude of the normal and frictional forces as well the components in the x and y directions. It also gives the inward force needed for this motion to occur.

To see how this works, adjust the speed of the car to be 8.6 m/s, set the bank angle at 22.5 degrees, the radius of the turn at 60 m and set m = 0.48. If you open up the calculations panel you should see something similar to what is shown to the left.

  1. For example, in order to travel at 8.6 m/s in a 60 m radius turn requires an inward force of:

=(1000 kg)(8.6m/s)2/(60.0 m) = 1233 N

  1. It is also easy to see that the sum of the upward components of both the Normal and Frictional forces equals the weight of the car (8809.17 N + 1000.83 N = 9810.0 N)
  2. Also, since the frictional force acts up the plane, it follows that the difference between the x-components of the Normal and Frictional forces equals the inward force (3648.88 N - 2416.21 N = 1232.67 N).
   

How to Set the Radius of the Turn

The radius of the turn can be adjusted by "grabbing" the outer tip of the red radius line and dragging outward (increase) or inward (decrease), toward the center of the turn. The radius will change in steps of 1 m.

This will have direct impact on the size of both the frictional and normal forces and you may want to adjust the radius and observe how these forces change. You can carry out this change even while the applet is running and observe directly the effect this will have on the motion of the car. To observe how the radius of the turn affects the size of some of the forces in this applet you should practice adjusting the radius and then observe the change in both the FBD and the calculations that appear in the Show Calculations Panel.