# Nonzero net force involving no displacement. Is this accurate?

1. Aug 5, 2013

### hondaman520

So I am studying mechanical engineering, and I got into a debate with my (mit mechy) graduate roommate about the possibility of having a net nonzero force which involved no actual displacement of an object.

Normally, when an object is accelerated along a direction (given an external force), it will be displaced.

I was thinking about an applied situation where a car makes a circular turn (uniform rotational motion, assuming there is no rotational acceleration), and there appears to be a nonzero net force along the direction orthogonal to the direction of travel. Obviously there is a centripetal force acting to keep the car planted on the road, directed in a circle. Textbooks describe the static friction from the tires, as the supply for centripetal force. And since the centrifugal (outward) force is only fictitious, there is a nonzero net force (centripetal), lateral to the direction of travel.

The interesting thing about this situation is that static friction involves no displacement of an object. However, centripetal acceleration is taking place, so it appears you can have a net acceleration, without actually being displaced in the respective direction.

Is this true? If so, could I also say, in theory, that there is no energy transfer? Because there is no actual work being done when the centripetal force (static friction) keeps the car directed along a circle.

I understand that in reality there is always energy transfer, due to slippage, other sorts of forces, etc. I am talking in theory here. My point is that, it seems that centrifugal force being only ficticious, which would balance out the centripetal force, does not exist in the total force equation, so there is a net force of static friction directed towards the center.

Also, if this is an accurate comprehension, why would it be considered accelerating, with a numerical magnitude in meters/secondsquared, when there is actually no displacement. This seams very counter-intuitive.

Please, I understand this was lengthy, but I am struggling to find professors who can understand my question. Any elaboration would be much appreciated.

2. Aug 5, 2013

### ModusPwnd

I think its odd to compare force and displacement. Force is an instantaneous value. You dont add it up over time. Displacement is not an instantaneous value. It is a difference of two instantaneous values. You can invent any situation you like here, zero force at each moment and non-zero displacement, non-zero force at each moment and zero displacement or whatever in between.

I'm not sure why you are referring to static friction for a case of circular or rotational motion. If you are talking about motion and friction you should be talking about kinetic friction. (oh, because of tires, I see)

Last edited: Aug 5, 2013
3. Aug 5, 2013

### PhanthomJay

The car is constantly accelerating toward the center by the centripetal acceleration due to the change in direction of the tangential velocity, causing the net centripetal static friction force acting toward the center, but the tangential velocity of the car keeps it in circular motion. If the car was not rotating about the center, there would be no centripetal force. The problem is similar to an astronaut orbiting earth....his/her acceleration is 'g' for that altitude inward, in free fall, but the tangential velocity keeps the astronaut in orbit preventing the astronaut from crashing into earth. In both cases, the car or astronaut is being displaced as they move in a circular path. And with no energy transfer, since no work is being done and the kinetic energy remains constant, with energy conserved.

4. Aug 5, 2013

### WannabeNewton

Acceleration doesn't require movement in the direction of acceleration. Yes there is no radial movement in this scenario but there is still tangential movement due to the traversal of a circular arc; the radial acceleration is perpendicular to the velocity so all it does is change the direction of velocity.

5. Aug 5, 2013

### Staff: Mentor

If you have a net force then the center of mass is accelerating. If the body is not rigid, then the fact that some part of it is stationary does not prevent the center of mass from accelerating.

6. Aug 6, 2013

### hondaman520

Thanks everyone for the input! This is really helping me conceptualize this.

I think my confusion was from me clinging to the tendency of a force to move something a given distance. Where if the distance moved is in a circular direction, there's really no displacement involved, whatsoever.

I still find it interesting, that a continuous force being applied to an object will not necessarily cause that object to speed up or slow down, in which case this is true, it is being applied 100% in order to change the direction of the object.

So a force can be applied (in a particular direction) do either two things, or a combination of both:

1. slow down or speed up the object (im talking magnitude here, not velocity).
2. change the direction of an already moving object.
3. A combination of 1 and 2.

Could someone verify this?

Update: I just read wikipedia, and it pretty much said this almost in exact same words.

"A force is any influence that causes an object to undergo a certain change concerning:

movement.
direction.
geometrical construction."

Or any combination of those 3 things (I would assume).

Last edited: Aug 6, 2013