Adjusted vehicle acceleration up an incline

[raverix]

Homework Statement

I need to come up with a general formula that a vehicle with given mass(m), friction coefficient(u), acceleration force(f), and slope(theta), return the amount of acceleration on the vehicle.

Homework Equations

max acceleration on an incline = -mgsin(theta) + (umgcos(theta))/m

The Attempt at a Solution

Following the information here, https://www.physicsforums.com/showthread.php?t=235128 I believe the equation for the maximum acceleration up an incline, = -mgsin(theta) + (umgcos(theta))/m, but this is just the maximum possible given the friction. I need to scale this down depending on the how much force the vehicle can put out.

Any suggestions on the next step, or am I going about this the wrong way?

 

[Redbelly98]

As you're probably aware, the maximum friction force is

F_max = μ_s N​

I think that expression would just be replaced with the (presumably lower) force the vehicle's engine is capable of.

 

[raverix]

I was under the impression that it would be more complicated, namely, that the force that the car could put out would get less and less as the slope increased, now I'm thinking this was where I was mistaken. The force that the vehicle can put out doesn't decrease until the vehicle's force exceeds the maximum friction force, so the solution, will look something like this...

if VehicleForce > MaxFrictionForce
max acceleration on an incline = -mgsin(theta) + (umgcos(theta))/m
if vehicleForce <= MaxFructionForce
max acceleration on an incline = -mgsin(theta) + vehicleforce

Sound right?

 

[Redbelly98]

Seems right, just be careful with the m's. I.e., mgsinθ is a force, not an acceleration ... just need to remove the mass from that term.