Solving Physics Assignment: Car Acceleration in Uniform Plane

[physicsA380]

hi, i am new to physics forums. forgive me if i post the thread in wrong forum.
i have a question regarding my assignment.
Q: a car travels in a uniform plane whose coeff. of friction is A. the max. acceleration that the car can have is Ag, where g is acceleration of gravity.Explain. [university physics, 4-6]
i would appreciate any help. thanks

 

[Doc Al]

What forces act on the car?

How can you use the coefficient of friction to calculate the friction force?

 

[physicsA380]

What forces act on the car?

How can you use the coefficient of friction to calculate the friction force?

as far as i know, the forces would be weight of the car, normal rxn from surface and friction..we will be neglecting all other forces like air resistance and so on...

i think max frictional force= coeff. of friction *normal rxn.
and we are talking about a level road. so i presume max. friction would be coeff of frc. * acc. due to gravity ( assuming mass of car=1 kg).
but i can't figure out why the acc. of the car can be no more than A*g, where A is coeff. of friction and g is acc. due to gravity.

thanks for help

 

[Doc Al]

as far as i know, the forces would be weight of the car, normal rxn from surface and friction..we will be neglecting all other forces like air resistance and so on...

Excellent.

i think max frictional force= coeff. of friction *normal rxn.
and we are talking about a level road. so i presume max. friction would be coeff of frc. * acc. due to gravity ( assuming mass of car=1 kg).

Good. But instead of assuming a mass for the car, call the car's mass "m". What's the max friction force then?

but i can't figure out why the acc. of the car can be no more than A*g, where A is coeff. of friction and g is acc. due to gravity.

You've found the max friction force (the only horizontal force acting on the car); now find the associated max acceleration. Use Newton's 2nd law.

 

[physicsA380]

i think i got it...what happens if they made a very powerful engine...would the car skid if the engine is put on full power...

thanks

 

[Doc Al]

Yes it would. If you apply more torque to the wheels than friction can deal with, the tires have no choice but to slip along the road surface.

The same thing can happen when braking, if you brake too hard. If you slow the wheels down faster than friction can deaccelerate the car, then the tires slip. Slipping is bad because you exchange static friction for kinetic friction, which provides less force with which to control and slow down the car. That's why (at least in older cars) you shouldn't "jam on the brakes" to stop--if you push too hard you start to slip and lose static friction. This is called "locking the brakes". Most cars these days come with "anti-lock" brakes that sense and prevent slipping better than a person can. (With ABS it's OK to jam on the brakes in an emergency.)