# Is the work done by friction on an accelerating car zero?

Consider a car is accelerating and its tires are not slipping ,just rolling.what is the force on the car that changes its kinetic energy? Some people say in the definition of work dw=F.dx that dx is the displacement of where the force is applied, so the work of friction on the car is zero becouse the down surface part of tires dont move with respect to road.is this correct? I think that work energy theorem states that the work of external forces on a body equls the change in the kinetic energy of center of mass,not where the force is applied.

please tell me if the work done by friction is zero,and our system is the car with its tires,which force cause the change in the kinetic energy of center of mass of the car?is its work zero?why? If zero how to justify work energy theorem?

(Be careful not to use the internal force for this theorem becouse best cars with best engines cant move on a sliding road like greasy road!the internal force cause if friction exist the care moves)

• It is not correct. You have to take the compression of the tires and the road surface into account, then there is the friction in the axle bearings and also the aerodynamic drag. All of these add up to an effective drag/friction force that points opposite to the motion of the car. – CuriousOne Feb 29 '16 at 7:11
• Please read here too physics.stackexchange.com/q/2451 – adel Feb 29 '16 at 7:18
• That one isn't correct, either. – CuriousOne Feb 29 '16 at 7:40
• You are great:) please write a complete answer if you had time.tnx – adel Feb 29 '16 at 7:49
• The comment contains all you need to consider. – CuriousOne Feb 29 '16 at 7:51

## 2 Answers

If the question is, "what work does the frictional force of the road do on the car?", then your original interpretation is correct. The road exerts a forward force on the car. This, combined with other forces acting (externally) on the car results in forward displacement of its center of mass, which counts as work.

The way you can show what you want to show is to first write the force balance equation on the car (including only external forces), and then dot the force balance with the instantaneous velocity vector of the center of mass of the car. This accounts for the translational kinetic energy of the car and will give you your work-energy equation immediately.

The "internal force" you talked about creates a torque on the wheel, which would try and cause slipping as friction naturally tries to oppose it, it acts in a direction as to oppose relative slipping between two surfaces and force the car to move, Since there is no force in in horizontal direction and there is increasing velocity, Friction will do translation work definitely (linear velocity related), if the wheel is supposed to roll purely, the angular velocity will also increase Here, as the direction of angular velocity is same direction as torque of internal forces, Both do work but friction does less and internal does more. The case that you are talking about is the NET work done by friction, ofcourse if the tyres are purely rolling, the point on the bottom is at rest and W=F.dx and instantaneously, displacement is always zero. So, net energy acquired by wheel is purely supplied by internal forces

• I said consider the whole car with its wheels as a system not just its wheels . Secondly in the formula w=F.dx , dx is the displacement of the center of mass,not where the force is applied. Internal forces do not effect ,you can not lift your self by your hands . – adel Feb 29 '16 at 7:33
• To counter your statement about centre of mass, suppose there is a hinged rod, and we leave it to rotate in horizontal position, what would be the kinetic energy of rod when it is in vertical position? did the normal acting on hinge do any work? – Mrigank Feb 29 '16 at 7:36
• Internal forces don't do any work by themselves, they force friction to do the work for them by "distributing" it's energy among the translation and rotational energy of wheel by medium of friction, if there was no friction, the wheel WILL purely rotate where does the energy come from here? the fuel we burn is not completely lost in form of heat – Mrigank Feb 29 '16 at 7:39
• Also, the Hinge does the same thing friction does in car, it just changes form of energy supplied by gravity – Mrigank Feb 29 '16 at 7:43
• So what cause the change in the translational kinetic energy of the car? The internal forces?isnt the work-energy theorem for external forces? – adel Feb 29 '16 at 7:45