Natural Science Forum / Physics / General Physics / June 2008

On Jun 28, 2:05 pm, zxcv_...@hotmail.com wrote:

Einstein showed us that directions in curved space are curved whether
he realized it or not. Your measuring rod is curved because it is
extended in the curved space-time continuum of gravity.

Movement and extension are in curved space.

Mitch Raemsch

On Jun 28, 6:05 pm, zxcv_...@hotmail.com wrote:

Gravity only "acts" in one direction.  Any other consideration you're
discussing here is a projection of the gravitational acceleration
vector into any arbitrary direction along which an object is free to
move.  Since a physical object can only move in one direction at a
time, no summations are required.  Now, the path that the object is
taking may not be static, and hence the projection may change as
needed, such as on a surface of non-constant slope.  But again, no
summation is required, since at any given instant, an object is still
only moving in one particular direction and there's still only one
projection angle.

I think you've misunderstood why we take components of the gravitational
force in those sort of problems, and what it means.  Neglecting friction,
there are *two* forces on a block sliding down an inclined plane, gravity
and the force of the inclined plane on the block.  Gravity is pulling
straight down, but the block can't move straight down without bending the
inclined plane.  The inclined plane does bend ever so slightly, and as a
result of that strain it puts pressure on the block.  The inclined plane
bends just enough so that the total force on the block is in a direction
which won't send the block through the inclined plane.

Here's a picture of the two forces on the block:

http://img168.imageshack.us/img168/652/forcescx1.png

The force of the inclined plane on the block is called the "normal force"
because it's normal (perpendicular) to the inclined plane.

And here's a picture of the total force on the block, obtained by adding
the two force vectors head-to-tail:

http://img510.imageshack.us/img510/6439/totalzd7.png

Notice that the total force is parallel to the inclined plane.  If the
normal force was just a little bit smaller, the total force would be
pushing the block further into the inclined plane, causing the normal force
to continue increasing.  If the normal force was a bit larger, it would
push the block away from the inclined plane, decreasing the normal force.
At this point, the normal force is stable.

You can see from the diagram that the total force and the normal force make
a right angle, and that the hypotenuse of the right triangle they form is
the gravitational force.  Thus, the total force is equal to component of
the gravitational force parallel to the inclined plane, and the normal
force is -1 times the perpendicular component.  But these are just
mathematical, geometrical statements, and they don't tell you the physics
of what's going on.  For that, you have to understand the two forces on the
block.

In general, when you solve problems like this, it's a good idea to:

(1) Draw a diagram showing the forces on the object.

(2) Then use the geometry of that diagram to calculate what the forces are.

You should *never* try to short-circuit the diagram by saying things like,
"Oh, the force on the block is the component of the gravitational force
parallel to the inclined plane," because you don't know if that's true
until you've looked at the forces.  Many students get into trouble this
way.

I hope this helps.  Good luck!

One hopes you are not in college.  If in college, one hopes you are
someplace harmess like home economics, fine arts, or political
science.  Why be a one-eyed man amidst the blind?

a = g[sin(theta)] where a = net downward acceleration, g = 9.8
m/sec^2, and "theta" is the angle of elevation.  Are you a diversity
admission?

Knowing something is insufficient.  You must know what you know -
understanding.