What is the max acceleration?

Question

A Car with four wheel drive has mass m=1000 kg. Its weight is evenly distributed among the four wheels, whose coefficient of static friction with the road =0.80. If the car starts from rest and the road is horizontal calculate the maximum acceleration it can attain without spinning its wheels?

Answer 1

Ffriction = Fnormal x coeffictient (u from now on)
Fnormal = Fgravity (because there is no vertical acceleration)Fnormal on each tire would be above Fnormal/4 = 2450 N
Ffriction on each tire = (2450)(0.8)

Ffriction = 1960 N on each tire

This is the max force you can have before it will begin kinetic friction (spinning its wheels).

Fnet = Ffriction x 4
Fnet = ma
7840 = 1000a
a = 7.84 m/s/s
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Not to be mean to grelan, but he messed up at the end.

he went from 800g = 1000a to a = 1.25, i think he was thinking of 1/8 which is 0.125.

besides that error he was correct.

Answer 2

the normal force on each of the wheels is : 1000*g/4 where g is the gravitational acceleration.

so, the maximum friction force on each wheel can be: 0.8*1000*g/4
= 800*g/4

this is the maximum force each wheel can push the car with, for a total force of 800*g

F=ma, so 800*g=1000*a
and:
a=1.25*g. if we take g to be 10m/s^2

a=12.5 m/s^2

Answer 3

So as not to confuse the asker, let me comment on the solution of Grelann.

800g=1000a

this is according to Grelann as you will see in the bottom part of his solution, and I agree. But in the simplification, I think he did it too quickly and stumbled.
The correct simplification should be:

a=800g/1000
=0.8g

and if we accept g=10m/s^2

then a=0.8*10
=8m/s^2