How to Draw a Vector Diagram for a Vehicle Moving on a Curved Banked Road? (Smarter Techniques)

 

Author:
Prof. Kali C. S.
M.Sc., M.Ed., D.C.S.
50+ Years of Experience in Physics Teaching

1. Introduction:

      Vector diagrams are one of the most important tools for understanding physics problems.
Many students often ask:

“How do I draw the vector diagram of a vehicle moving on a banked curved road?”

    Where to start? How to show the forces? Which vector should come first?

    In this blog, we will learn a simple, neat and smarter technique to draw this diagram—perfect for Class 10–12 students.

2. What is a banked road?

   Banking means making the road bed slightly inclined to the horizontal. This is done at curved roads for safe driving.

3.Forces Acting on a Vehicle on a Banked Curve:

   Fig. A

    Fig. A represents a cross section of a banked road along with a vehicle on a curved road.

Consider a vehicle of mass m moving with velocity v on a curved road of radius r and banked at an angle of Ө.

Two major forces act on the vehicle:

(i) Weight (mg) acts vertically downward.

(ii) Normal Reaction (N) acts perpendicular to the inclined surface.

     The normal reaction by the roadbed on the vehicle N is resolved into NsinӨ and NcosӨ.

NsinӨ acts as a centripetal force  mv² / r  on  the vehicle.

∴  NsinӨ = mv² /r

And NcosӨ  is balanced by the weight of the vehicle,

NcosӨ = mg = weight of vehicle.

Using these equations we get:

v²  = r. g.tan Ө

This equation helps us find the safe velocity for the vehicle on a banked curved road.

4. How to draw the vector diagram? (Step-by-step):

(Smarter Techniques for Physics Diagrams)

Follow the steps below to draw a clean, examination-perfect vector diagram.

✔ Step 1: Draw the inclined plane:

• On an A4 sheet, take a point A near left side, draw full horizontal line from A, and then draw a slanted line slightly making the angle θ to horizontal. .
• This represents the banked road.

✔ Step 2: Mark the vehicle:

• Draw a small rectangle or dot on the surface (slanted line)
• Mark point O at the centre of rectangle.
• This point represents the centre of gravity of the vehicle.

✔ Step 3: Draw the normal reaction (N):

• From the same dot O, draw an arrow perpendicular to the inclined plane.
• Label it N.

(Most students make mistakes here—normal reaction is always perpendicular to the surface.)

✔ Step 4: Resolve the normal reaction:

Draw two components of  N with arrow heads:

• N cosθ → vertically upward
• N sinθ → horizontally towards the centre of the circular path

Make both components as the sides of parallelogram and complete parallelogram.

✔ Step 5: Draw the weight (mg):

• From the dot O, draw a vertical downward arrow equals to N cosθ line .
• Label it mg.

✔ Step 6: Show the direction of Centripetal force:

• The arrow headed N sinθ line represents centripetal force.
• Label: Centripetal force = mv²/r

✔ Step 7: Neatness and final touches:

• Show the angle θ clearly
• Keep all arrows emerging from the same point
• Align arrows straight and sharp
• Recheck labels and arrow directions

Your vector diagram is ready!

5.  Video  Support:

   So do you want to know ‘How to Draw a Vector Diagram for a Vehicle Moving on a Curved Banked Road’ using given guidelines?

Let us learn with the help of the following video, the actual smarter method of drawing the diagram.