Acceleration Inclined Plane

It is also called a ramp. The plane which is inclined is one of the six simple machines. Objects which are placed on an inclined plane accelerate due to a force which is unbalanced. In this article we will analyze the motion experienced by an object placed on a plain which is inclined.

Normal Force 

The force which is a normal force in an inclined plane is not directed in the direction that we are accustomed to. We have up till now always seen normal force directed upwards in the direction which is opposite to the force of gravity. 

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Gravity Force

To find out the net force which is acting upon an object on an inclined plane is difficult because the two forces that are already acting on the body are not opposite in directions. To simplify this whole thing one of the forces acting on the object will have to be resolved into direction which is perpendicular components so that they can be added to other forces. The force that is directed at an angle to the horizontal of the plane is resolved into vertical and horizontal components. In the case where inclined planes are there, we resolve the weight of the vector that is Fgrav into two components. The gravity force will be resolved into two components of force again that are – one which is directed parallel to the inclined surface and the other- which is directed perpendicular to the inclined surface. 

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Simplifying Problems of Inclined Plane 

In the friction or the presence of friction or other forces that are applied force or the tensional forces etc  a slight situation is more complicated. Consider the diagram shown below. Yet the force which is frictional force must also be considered when determining the net force. As in all problems of net force, the net force is the vector sum of all the forces which are present. That is we can see that all the individual forces are added together as vectors. The components which are perpendicular and the normal force add to 0 N. The components which are parallel components and the friction force add together to yield 5 N. The net force is 5 N, which is directed and the incline towards the floor.

The above problem and all planes which are inclined plane problems can be simplified through a useful trick which is known as "tilting the head." So to transform the problem back into the form with which we are more comfortable merely tilt our head in the same direction that the incline was tilted. Or we can do other better things yet merely tilt the page of paper and a sure remedy for TNS - "tilted neck syndrome" or "taco neck syndrome" so that the surface no longer appears in the level it was earlier. 

This is illustrated in the below diagram: 

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Acceleration 

In mechanics the process of acceleration is the rate of change of the velocity of an object with time. Accelerations can be determined as they are vector quantities in which they have magnitude and direction. The object's orientation acceleration is given by the orientation of the net force which is acting on that object. The objects magnitude acceleration as described by sir Newton's Second Law is the combined effect of two causes mentioned below:

• The balance which is net balance of all external forces that are acting on that object — magnitude is directly proportional to the net force

• That mass of object which is depending on the materials out of which it is made — magnitude is inversely proportional to the mass of the object.

If we see the example when a vehicle starts from a standstill position that is zero velocity in an inertial frame of reference and travels in a straight line at increasing speeds and it is accelerating in the travel direction. 

In an Inclined Plane Forces and Acceleration 

A mass of 4 kg is released on a frictionless slope which is at an angle of 30o to the horizontal.  Gravity here which causes the mass to accelerate down from the slope.  But the force of gravity or W which acts vertically downwards itself.  So the force causes the acceleration  component of the force of gravity acting down the slope denoted by  (FD).

The gravity  force is resolved into two components that are denoted as  FD and which is parallel to the slope which is  FP perpendicular to the slope.

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Here W = mg = 4 x 9.8 = 39.2 N

Here FD = mg sin 30o = 39.2 x sin30o = 19.6 N

Here FP = mg cos 30o = 39.2 x cos30o = 33.9 N

And FP presses the object and that too against the slope and it is balanced by the normal reaction force that is denoted as R.the unbalanced force which is causing the acceleration that is FD.

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