Truck accelerating up/down on wedge with friction.

• nickclarson
In summary, the coefficient of static friction (\mu_s) between a truck and road surface is used to determine the maximum acceleration of a four-wheel-drive truck of mass M on an inclined road surface with angle \theta. When the truck is climbing or descending, the direction of the frictional force is always opposite the direction of motion. The engine is not taken into account unless specified in the problem. Remember that the net force on the FBD should only include forces that are acting on the truck at that specific moment in its movement.
nickclarson

Homework Statement

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

a). Climbing

b). Decending

Homework Equations

$$\textbf{F}_{s}$$ = $$\mu$$$$_{s}$$$$\textbf{F}_{n}$$

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.

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
Code:
[ tex ]...[ tex ]
thingy. For example, instead of using separate things, in just one of them you can write

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

which will produce

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

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 :)

1. What is the purpose of studying truck acceleration on a wedge with friction?

The purpose of studying truck acceleration on a wedge with friction is to understand the principles of motion and forces involved in this scenario. This can help in designing efficient and safe transportation systems and vehicles.

2. What factors affect the acceleration of a truck on a wedge with friction?

The acceleration of a truck on a wedge with friction is affected by the mass of the truck, the angle of the wedge, the coefficient of friction between the truck and the wedge, and the force applied to the truck.

3. How does friction impact the acceleration of the truck on the wedge?

Friction plays a crucial role in slowing down the truck's acceleration on the wedge. It creates a force that opposes the motion of the truck, making it more difficult for the truck to move up or down the wedge.

4. Can the truck accelerate downwards on the wedge with friction?

Yes, the truck can accelerate downwards on the wedge with friction if the force applied to the truck is greater than the force of friction. However, the acceleration will be slower compared to the acceleration when moving upwards on the wedge.

5. How can we minimize the impact of friction on truck acceleration on the wedge?

To minimize the impact of friction, we can reduce the coefficient of friction between the truck and the wedge by using materials with lower frictional properties. We can also reduce the angle of the wedge and increase the force applied to the truck to overcome the force of friction.

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