# Relationship between centripetal force and mass

### What is a centripetal force? (article) | Khan Academy

The centripetal force depends on the mass of the object speed of the object its from Five trials were done to achieve high precision and accuracy among the. This is sometimes referred to as the centripetal force requirement. The word . where the Theta in the equation represents the angle between the force and the. Learn what centripetal forces are and how to calculate them. neither mass is moving vertically and there is minimal friction between the string and tube?.

During the turn, the car travels in a circular-type path. That is, the car sweeps out one-quarter of a circle. The friction force acting upon the turned wheels of the car causes an unbalanced force upon the car and a subsequent acceleration. The unbalanced force and the acceleration are both directed towards the center of the circle about which the car is turning. Your body however is in motion and tends to stay in motion.

It is the inertia of your body - the tendency to resist acceleration - that causes it to continue in its forward motion. While the car is accelerating inward, you continue in a straight line. If you are sitting on the passenger side of the car, then eventually the outside door of the car will hit you as the car turns inward. This phenomenon might cause you to think that you are being accelerated outwards away from the center of the circle.

In reality, you are continuing in your straight-line inertial path tangent to the circle while the car is accelerating out from under you. The sensation of an outward force and an outward acceleration is a false sensation.

There is no physical object capable of pushing you outwards. You are merely experiencing the tendency of your body to continue in its path tangent to the circular path along which the car is turning. You are once more left with the false feeling of being pushed in a direction that is opposite your acceleration.

The Centripetal Force and Direction Change Any object moving in a circle or along a circular path experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle. This is the centripetal force requirement. The word centripetal is merely an adjective used to describe the direction of the force. We are not introducing a new type of force but rather describing the direction of the net force acting upon the object that moves in the circle.

Whatever the object, if it moves in a circle, there is some force acting upon it to cause it to deviate from its straight-line path, accelerate inwards and move along a circular path.

Three such examples of centripetal force are shown below. As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion. As a bucket of water is tied to a string and spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion.

As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion. The centripetal force for uniform circular motion alters the direction of the object without altering its speed. The idea that an unbalanced force can change the direction of the velocity vector but not its magnitude may seem a bit strange. How could that be? There are a number of ways to approach this question. One approach involves to analyze the motion from a work-energy standpoint.

## The Centripetal Force Requirement

Recall from Unit 5 of The Physics Classroom that work is a force acting upon an object to cause a displacement. As the centripetal force acts upon an object moving in a circle at constant speed, the force always acts inward as the velocity of the object is directed tangent to the circle.

This would mean that the force is always directed perpendicular to the direction that the object is being displaced. The angle Theta in the above equation is 90 degrees and the cosine of 90 degrees is 0. Thus, the work done by the centripetal force in the case of uniform circular motion is 0 Joules.

Recall also from Unit 5 of The Physics Classroom that when no work is done upon an object by external forces, the total mechanical energy potential energy plus kinetic energy of the object remains constant. So if an object is moving in a horizontal circle at constant speed, the centripetal force does not do work and cannot alter the total mechanical energy of the object.

For this reason, the kinetic energy and therefore, the speed of the object will remain constant. The force can indeed accelerate the object - by changing its direction - but it cannot change its speed.

### Centripetal Force: Definition, Formula & Examples - Video & Lesson Transcript | nickchinlund.info

In fact, whenever the unbalanced centripetal force acts perpendicular to the direction of motion, the speed of the object will remain constant.

For an unbalanced force to change the speed of the object, there would have to be a component of force in the direction of or the opposite direction of the motion of the object.

Applying Vector Components and Newton's Second Law A second approach to this question of why the centripetal force causes a direction change but not a speed change involves vector components and Newton's second law. The following imaginary scenario will be used to help illustrate the point. Suppose at the local ice factory, a block of ice slides out of the freezer and a mechanical arm exerts a force to accelerate it across the icy, friction free surface. Last week, the mechanical arm was malfunctioning and exerting pushes in a randomly directed fashion.

## What is a centripetal force?

The various direction of forces applied to the moving block of ice are shown below. For each case, observe the force in comparison to the direction of motion of the ice block and predict whether the force will speed up, slow down or not affect the speed of the block. When an object is traveling in a circular path, centripetal force is what keeps it fixed in that path. Learn more about this force, how it is calculated and examples of its occurrence.

A quiz is provided to test your learning. Definition of Centripetal Force Do you remember riding on the merry-go-round as a kid? Did you ever stand at the very edge of the merry-go-round and hold on tight to the railing as your friends pushed the wheel faster and faster? Maybe you remember that the faster the wheel turned, the harder it became to hold on.

You might not have known it at the time, but you were creating a balance between two forces - one real and one apparent - in order to stay on that circular path. Merry-go-rounds are a perfect example of how a force is used to keep an object moving in a circular path. Your body wanted to fly off the merry-go-round in a straight line, but your hands exerted an opposing force to keep you on.

The tendency for your body to fly off the merry-go-round is called centrifugal force. It isn't a real force, but an apparent one.