Assume you are driving a very fast car on a straight road with no change in elevation. Lets make the flat road (and the surrounding flat desert) the XY-plane which makes the Z-axis straight up and straight down. Up ahead the road (no longer on the XY-plane) starts to slope downwards at an angle of 10 degrees (4/9*pi) relative to the XY-plane.
Assuming the acceleration of gravity is 9.8 m/s^2 regardless of elevation I presume that if one were travelling at a speed of 10 m/s and started accelerating by 56.44 m/s^2 (9.8/(sin 10 degrees)) then your acceleration in the negative Z direction would be 9.8 m/s^2 and you would be weightless and not be able to accelerate at any faster rate because your traction would be 0. Is this correct?
No. The acceleration due to gravity has a component 9.8*cos(10) perpendicular to the slope. Assuming that you’re accelerating parallel to the slope, that acceleration has no component perpendicular to the slope to counter gravity. So you’ll always feel a pull towards the ground.
If you had a rocket engine, and accelerated horizontally at 9.8/tan(10), that would provide a total acceleration (after including gravity) that is parallel to the slope, so you would have zero traction in that case.
The reason you have traction just sitting still on a level street is the car is trying to fall at 9.8 ms[sup]-2[/sup] and the road is getting in the way.
If the slope was dropping away in a more or less parabolic curve, you’d have no traction. (I say “more or less” to avoid air friction, rolling friction and other tiresome pedantries.) You’d be freefalling parallel to the slope with a constant horizontal speed equal to whatever you had at the moment you transitioned from the flat road to the dropping road. And your vertical speed would be increasing at 9.8 ms[sup]-2[/sup] the whole time.
So anything flatter than that parabolic drop off is going to produce more than zero traction because your vehicle is trying to fall faster than the road is dropping underneath you.
Would I be correct in guessing that this is a homework problem? If so, my first piece of advice would be to draw the free-body diagram of the car. And it’ll probably help to use a coordinate system lined up with the road instead of vertical and horizontal (which means you’ll need to break up the weight force into components).
I appreciate your advice but its not homework. Haven’t done homework in many years. I have been thinking about going back to school and try for my mechanical engineering degree again so I have been brushing up at Khan Academy. It was just a problem I made up while bored at work.