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Force Acting on an Inclined Plane

Force and Laws of Motion II - Concepts

Conservation of Linear Momentum

Principle of Conservation of Linear Momentum

Principle of Conservation of Linear Momentum and Newton Laws of Motion

Impulse

Impact Force

Newton Second Law of Motion and Equation of Motion

Force Acting on an Inclined Plane

Class - 9th Foundation NTSE Subjects

Concept Explanation

Force Acting on an Inclined Plane

The normal forces in an inclined plane are not always directed upward opposite to the direction of gravity but rather they are always directed perpendicular to the surface that the object is on. To understand the direction of the force acting on an inclined plane the force acting on the object will has to be resolved in two components.The force that is directed to an angle to the horizontal is resolved into horizontal and vertical components. This can be explained with the help of an example.

For example:

In the figure the object is moving down an inclined plane which is making an angle $;theta$ with the plane, with Force = f

The normal force = N and it is perpendicular to the plane

$F_w=mg$ is the weight of the load.

The component that balances the Normal force $=mg ;Cos;theta$

The component that is responsible for the sliding motion is $=mg ;Sin;theta$

In the absence of the friction and the other forces, the acceleration of an object is the value of the parallel component divided by the mass.It results in the equation as

$a:=:gsintheta$

In the presence of the friction and other forces such as applied force and tensional force, it gets slightly complicated.

Q 1. A five kg mass, initially at rest, slide down a friction less $30^{circ}$ incline.Calculate the force parallel to the incline and the acceleration of the mass . If the incline is 0.8 m long, calculate the velocity of the mass when it reaches the bottom of the incline.

Solution: We have to calculate force parallel to the incline , acceleration and the velocity of the mass

The force parallel to the incline , $F$ $=mg ;Sin;theta$ = (5)(9.8)(sin30) = 24.5 N downwards (sin 30 = 0.5)

Acceleration of the mass is , $a:=:gsintheta$ = (9.8)(sin 30) = $4.9;m:/s^2$

Velocity of the mass on reaching the bottom can be find out using equation

$v^2:=:u^2:+:2as$

Here, u = 0 , a = $4.9;m:/s^2$ and s = 0.8 m

So, $v:=:(2as)^{1/2}$

$v:=:(2as)^{1/2}:=:(2times4.8times0.8)^{1/2};=:2.8;m/s$

Q. A 2 kg mass is incline down an inclined plane with an unknown angle , as shown.The incline is assumed to be frictionless and is 1.2 m long. The mass start from the rest and is observed to take 2.3s to reach the bottom . What is the angle of incline?

Solution: A of the mass along the incline, $a:=:gsintheta$ $= (9.8)(sintheta )$ .....................(i)

We need to use this formula , $s:=:ut:+:frac{1}{2}at^2$

$a:=:frac{2s}{t^2}$

$a:=:frac{2times1.2}{(2.3)^2}:=:0.4.5:m/s^2$ .................(ii)

Now, from equation (i) and (ii) $0.45;=;(9.8)(sintheta ):=:0.046$

$theta :=;2.63^{circ}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Which of the following are correct : (a) In the absence of the friction and the other forces, the acceleration of an object is the value of the parallel component divided by the mass. (b) The normal forces in an inclined plane are not always directed upward opposite to the direction of gravity but rather they are always directed perpendicular to the surface that the object is on.
A. Only (a) is correct.		B. Only (b) is correct.
C. Both (a) and (b) are correct.		D. None of these.
Right Option : C
View Explanation

Question : 2

The normal forces in an inclined plane are not always directed ________________ to the direction of gravity.
A. upward opposite	B. opposite	C. downward opposite	D. None of these.
Right Option : A
View Explanation

Question : 3

The force that is directed to an angle to the horizontal is resolved into ____________________components.
A. Horizontal	B. Vertical	C. Both (a) and (b) are correct.	D. None of these.
Right Option : C
View Explanation