about the resultant force on a car round a bend?

Question

I wanted to know what is the resultant force on a car moving around a bend. My teacher says it is the centripetal force and it is directed towards the centre. But wait a second! If the resultant force is acting towards the centre of the circle, then the car should not have been able to move round the circle and should have move towards the centre of the circle instead. Since a resultant force causes a body to move in a straight line in the direction of the resultant force. What do you think??

Answer 1

Your reasoning is not correct.

You are assuming that the velocity of the car is in the same direction as the resultant force.

But since Newton we work with a model in physics where the *acceleration*, not the velocity, is in the direction of the force.

So if the resultant force points toward the center of curvature (your teacher is right in that), the car continually changes its direction toward the center.

However, it does not lose its original velocity. We call that "inertia". Inertia keeps the car moving in its original direction (straight line). The force pulls it toward the center. The net effect is circular motion.


This is precisely the reason why the moon circles around the earth. The only force on the moon is toward the earth -- and yet it does not fall.

Or think of what happens when you swing something around at the end of a string. The only relevant force is the pulling force on the string. Yet the object moves in a circular fashion.

Answer 2

A force causes an acceleration or change in velocity, but doesn't have to cause a change in the speed. You can change the direction of travel without changing the speed. Because the acceleration is always perpendicular to the direction of travel, it never adds or subtracts from the magnitude of the velocity. In other words, because the force vector is always toward the center of the circle (like a toy on a string), the speed never changes.

Now, the magnitude of the force has to be just right. If the force were too large or too small, the vehicle wouldn't travel in that particular circle. However, if the method used to apply the force is such that it will always be perpendicular to the path of travel (like turning the steering wheel on a car) then, the result will be circular motion.