A
block of mass M slides down a rough inclined plane of inclination Ѳ
with horrizontal, with initial velocity v and from a height h. At the
bottom point its velocity becomes zero. Then the work done by the
friction force in stopping the block
[Physics].... [Magazine - Engineering Success]....
Objective Type Answers Are
a) -(1/2mv2 + mgh)
b)1/2mv2 - mgh
c)2mgh - 1/2mv2
d)mv2 - mgh
answer as per the magazine……………………..[ANSWER (a)]
Lets assess ....
Friction Formula
This
can be the formula for friction for an real object which has weight m
in an inclined surface in front of the constant g. Meaning within a
earth within the scope of constant g.
Descriptive image
Here is the descriptive image that depicts the real scenario:
Fig. 1: Illustration picture1
Object
which has the weight m stands in the inclined plane of the angle Ѳ from
horizontal plane which has the gravity g; because of its friction, the
movement of the object can be denoted by the velocity v in the inclined
surface. And it is a try for the calculation of that friction
Physical properties taken for consideration:-
1)
|M| = m [Mass of the object. value m is absolute. For accurate
calculations m must have comprised with specific formula. But in front
constant g it can be represented just as weight m]
2) v - [is the velocity of the object. It is known that surface of the square plane can be v2 (if one side is denoted by v) so the possibility falls within v2 it
is nothing but possibility in logical plane in front of the constant g,
which (this plane) is not depicted in figure. But it can
understandable by a physicist. Maybe someone correct me if I am wrong.
And v can be very small as speed of the object is 0 w.r.t horizontal
plane
3)
h - [is the height from the ground for the object taken for
consideration. Reverse direction to the height g is applied for the
object all the time. So the constant g must be taken to consideration
whether it is about the motion or friction or whatever the physical
principal of the object]
4) g - [is the gravitational constant for the earth taken to the consideration]
5)
speed of the object with respect horizontal plane is 0, however v might
have some minute value as the object has mass m and g is applied all
the time. And again it is calculation for friction rather motion.
6)
Ѳ - [is the angle of actual inclination plane from the surface. The
intersection taken to consideration, the rectangle (supposed to be
square) is just to have proper f(x) for the object friction or motion or
whatever the physical principal. Here rectangle drawn will be
considered as square in front of the constant g]
and there are other constants and properties described as part of solution
Solution
ΔK = W
g + W
f
Change Possibility Constant = Weight of the object in a given gravity and height + Friction weightage
[It
is assumed that gravity g is evenly applied in the place taken for
consideration, Meaning it is not that big place where g gets out of its
scope]
- 1/2 mv
2 = mgh + W
f
ΔK is
represented in negative, as the speed of the object is 0 with respect to
horizontal plane. It is negative because it is ideal. Or this could be
the reason that force is applied reversely.
[Geniune
constant 1/2 is derived considering considerable amount of plane of the
square considering/ignoring the angle of inclination Ѳ. Surface of the plane is a2 = ax consider x is 2; considering Ѳ there can be slight difference, limiting scope, aΔx ; ∴ with respect f(x) (the ratio of) the scope of the difference in surface can be aΔy/Δx
(here Δy is the actual variance ); for the y unit 1, x must be and
always 2 (FOR THE CALCULATION OF PLANE SURFACE OF SQUARE); so it can be
limited by a1/2; This is how this constant 1/2 is derived considering g is good constant and Ѳ and
can be ignored in front of it for the scope taken for consideration.
However the formula might yield values only closer to the accurate value
which considers all the facts.]
[In other words a2 considering Ѳ inclination, (the ratio :- ) it can be a to the power of two inverse; 2-1=1/2]
[Or it just the half probability considered having the fact of inclination Ѳ from the horizontal plane]
[OR] The level obsession:-
As g is applied in the virtual plane radically evenly,
| [NOTE:
In general this logical planes are considered to derive an proper f(x),
rather to get more realistic 3D values just for a good assessment of
the context in science] |
->the surface of the square plane a
2
->can be ignored in the level base - a
->when we limit the scope considering/ignoring the inclination Ѳ, Δy/Δx => d/dx ax (=2)
-[To be written]-
∫ f(x).dx [also the scope can be limited between some range]
∫ a2.dx
=> 1/2.a3 [Nothing but the range can fall within the half cubic units]
in front constant g a3 can be ignored as it is equally dispersed.
1/2 is nothing but 2-1
we get constant 2-1
->and it is nothing but 1/2
->as the motion is in reverse, ΔK is represented in minus (-)
Wf = -(1/2mv2 + mgh)
Friction weightage or force = -(1/2mv2 + mgh)
HOWEVER, it is not accurate rather it is almost a closer value
Here is an example
It
might be photographic illusive holographic object from the camera's
flash in move around the sun, or could be an real object in move or it
could be electric inference but I have a little hope that this formula
might get apply as a base for the formula that yields correct &
accurate friction force. Maybe more consideration needed.
[Fig.]
