A block of mass M slides down a rough inclined plane of inclination Ѳ

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

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Contents

• Objective Type Answers Are
• Friction Formula
• Descriptive image
• Physical properties taken for consideration:-
• Solution
• [OR] The level obsession:-
• Here is an example

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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 mv² = 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 = a^x consider x is 2; considering Ѳ there can be slight difference, limiting scope, a^Δx ; ∴ with respect f(x) (the ratio of) the scope of the difference in surface can be a^Δy/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 a^1/2; 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 a²
->can be ignored in the level base - a

->when we limit the scope considering/ignoring the inclination Ѳ, Δy/Δx => d/dx a^{x  (=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 (-)

W_f = -(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.]