physics - vectors

[anthropos]

Please read the attachments. Thanks, dudes. The teacher just started on this topic, and I am still very unfamiliar with the chapter.

[Primarygun]

1. Consider on a table with a zero inclination.

Think about why the object is at rest on it, i.e. in its equilibrium.

In my case, by considering the Newton's first law, you know where the other force is.

It gives the hints to you.

2. For any force, you can always split it into x-component and y-component.

In this case, you may consider the direction along the surface of slope as x-direction.

With a right-angle between the forces you will draw, you will get the sum of the squares of them equals to F².

[DQW]

Anthropos, when the plane is described as "smooth" that means there's no friction. What's the other important force you're forgetting about ? What kind of force (actually it's a pair of forces) do you always have between two bodies that are pressing against each other ?

[DQW]

For part (b), you will not understand what it says unless you read what your textbook has to say about this (or the notes from when your teacher taught it in class) and look at some worked examples to see how it's done.

[blike]

Think about what force the incline is exerting on the block. There's a specific name for it. As DQW mentioned, its assumed there is no friction ("smooth surface").

[MetaFrizzics]

It might be easier for a student to approach this in two parts:

First the simpler case of the block on the inclined plane *without* any external forces:

 

 

Make an Assumption:

(1) Suppose the block isn't moving at all, but resting on the inclined plane. This means that the force of gravity is exactly balanced by a resisting counter-force from the solid inclined plane.

Parallelogram Law and Coordinate Systems

(2) Each force can be split into x', y' components, with the two axeese placed in any arbitrary orientation, at rest with the whole setup. Here we choose to orient the x'-axis in parallel with the inclined plane, and the y'-axis perpendicular to it. (This is a simple right-angle version of the Parallelogram Law for combining forces.)

 

First note that the gravity force can be seen as two parts or components, one force pressing directly on the plane, and the other pushing the block along the plane downward (blue downward arrows).

 

How to Deal with Passive Counter-Forces

The counter-forces are merely passive. We can assume since the plane is solid that it will always match the gravity component with an exact counter-force (but no more, since there is no active machinery). We can think of the counter-force upward from the plane as an 'infinite reservoir', since we don't forsee gravity actually winning by crushing the inclined plane. Thus since the forces perpendicular to the inclined plane always match and cancel, we can ignore them!

 

Now the question is, what about the gravity component pushing the block downward along the plane? If the block is not moving, then the only counter-force available is friction. This force is small relative to the direct pressure on the plane, so only a little friction will hold the block from sliding. (Again, *more* friction won't add an active force, just provide a reservoir of counter-force for a larger downward push).

 

That is, we can say that if the block isn't moving, the opposing friction is >= the downward force along the plane, and if the block slides, there isn't enough friction to hold it. We might even be able to calculate the friction by measuring the acceleration of the sliding block (but that's another question).

 

Eliminating Non-Existant Forces

(3) And now the 'trick' part of the question. It said 'smooth' surface, which we are supposed to interpret apparently as 'friction-free' or with insignificant friction. This means the smaller downward force component of the gravity force along the plane is unopposed, and the block will slide down the plane (it becomes the net force).

 

Note also that we treated the passive resisting forces each a bit differently, but intuitively, as the physical situation seemed to require. In one case we imagined an uncrushable ramp and infinite opposing force available, and in the other we assumed we *could* overcome the opposing force of friction at some unknown point (or incline).

 

Now we have all the tools and ideas with which to tackle the original question.

 

What You Needed to Solve This

a) A familiarity with the Parallelogram Law for Addition of Forces and graphical treatment of forces as vectors.

b) A familiarity with Coordinate Systems and Orthogonal Vectors/Directions. This is more than just adding vectors. You should understand why you are choosing right-angle vectors, and why you are choosing a certain orientation of the vectors when breaking down basic vectors into their components.

c) An ability to handle 'problem' forces like friction and passive resistance intuitively and accurately.

d) An ability to break the problem down into simpler components or isolated parts and solve a step at a time.

 

Notes for Later

Later on in your course, you may be revisiting this question with more information. For instance, you may have to find the net force, then calculate the expected acceleration of the block sliding down the plane, or vice versa: You may be given the acceleration of the block, and have to calculate the force. In these cases, you'll use differentiation or integration to move from one answer to the other.

[anthropos]

OMG O_O, thx Metafrizzics...and all the great guys in this thread

[MetaFrizzics]

Don't forget to note the errors in your first diagram:

 

(1) The friction force is pointing the wrong way.

 

(2) Apparently there is no friction force in this question!

 

(3) You didn't take notice or remark on the simple opposing force of the ramp.

 

(4) You failed to break down the gravity force into (useful) components.

 

Don't worry that it all seems overwhelming the first time you deal with these things. I wouldn't have got the 'smooth' surface thing myself in your shoes. It seems perplexing how people 'know' how to divide up or break down forces into the right components at first. This comes with some experience looking at answers to these questions, solving a few yourself, and finding people who can explain what the essentials of the problem at hand actually are.