Truck accelerating up/down on wedge with friction.

[nickclarson]

Homework Statement

The coefficient of static friction between a truck and road surface is [tex]\mu[/tex][tex]_{s}[/tex]. What is the maximum acceleration of a four-wheel-drive truck of mass M if the road surface is at an angle of [tex]\theta[/tex] with the horozontal when the truck is...

a). Climbing

b). Decending

Homework Equations

[tex]\textbf{F}_{s}[/tex] = [tex]\mu[/tex][tex]_{s}[/tex][tex]\textbf{F}_{n}[/tex]

The Attempt at a Solution

I figured out the solution some how by magic but I really don't understand it fully. My problem is just setting up the free body diagram in general and knowing which direction the frictional force is pointing. I was also having trouble in knowing whether or not to include the force of the engine driving the car on the FBD.

 

[foxjwill]

Unless it says so in the problem, assume that the engine is not taken into account. And the direction of the frictional force is always opposite the direction of motion. For example, when the car is descending (i.e. the direction of motion is pointing down the incline), the force of friction is directed up the incline.





Just as a side note, you can include the entire equation in one

[ tex ]...[ tex ]

thingy. For example, instead of using separate things, in just one of them you can write

 \mathbf{F}_s = \mu_s \mathbf{F}_N

which will produce

[tex]\mathbf{F}_s = \mu_s \mathbf{F}_N[/tex]

 

[nickclarson]

Ohhh ok, I was just assuming that I should take the engine into account because the truck is accelerating and moving in one direction. Isn't the acceleration and movement of the truck a net force that should be added to the FBD? OR are we just looking at the truck at one point in it's movement. Not sure, confused.

I also thought that in the first part, even though the truck is moving upward, it is trying to slide down so the frictional force would point upward. I guess I just need to remember that it always opposes movement.

Thanks for that latex help :)