Inclined Plane is the most fundamental forms of mechanical devices used in physics. In order to get around physical obstacles and simplify tasks, inclined planes have been used for centuries in both ancient and recent construction projects. A flat surface that is angled with respect to the horizontal plane is the fundamental component of an inclined plane. It is a basic mechanism that works by extending the force over a greater distance in order to decrease the force required to move an object vertically.
In this article, we will learn in detail about inclined plane, the mechanics behind it, the resolution of forces into horizontal perpendicular component acting on inclined plane and solve examples based on it.
What is Inclined Plane?
Inclined Plane in physics can be considered as basic machine with a flat surface angled at an angle towards the horizontal plane. It offers an approach of lifting objects while using less force than necessary to raise them vertically. There are many applications of inclined planes such as ramps, hills, and even the inclined surfaces of staircases. They spread the labour over a greater area, enabling things to be moved up or down with less force.
Mechanics of Inclined Planes
An inclined plane's main function is to promote the shifting of items vertically by applying force horizontally. The longer the inclined plane, the less force is required to lift an object. This principle is fundamental to understanding how inclined planes work and why they are useful in various applications.
When an object needs to be moved vertically, such as lifting a box onto a shelf, the force required to overcome gravity directly is significant. However, by using an inclined plane, the force needed to lift the object vertically can be reduced. Here's how the mechanics of inclined planes work:
Force Distribution: When an object is placed on an inclined plane, the weight of the object acting downwards results in one component of the force of gravity acting on the object to be parallel to the surface of the inclined plane, and the normal force exerted by the inclined plane upwards is the other component that can be resolved into two parts. It is possible to separate the object's weight into two parts: one that is parallel to the inclined plane and the other that is perpendicular to it.
Reduction of Force: The movement along the inclined plane is distinct of the part of the object's weight acting perpendicular to it. As a result, the movement is only affected by the weight component parallel to the inclined plane. This indicates that, in comparison to raising the object vertically, less effective force is required to move it along the inclined plane.
Mechanical Advantage: The mechanical advantage of an inclined plane is calculated by finding the ratio of the length of the inclined plane to its height. A longer inclined plane requires less force to move an object along its length. This is because the longer length allows the force to be applied over a greater distance, reducing the force needed to overcome gravity.
Friction: Movement of the object may be affected by friction between it and the inclined plane. By giving friction and stopping the thing from sliding too quickly, friction can be helpful. On the other hand, too much friction can make things difficult to move and need more force to overcome.
Angle of Inclination: The efficiency of the inclined plane also gets affected by the tilt angle. Up to a certain point, the force needed to move an item along a plane decreases as the angle of inclination increases. After that, the effort needed can rise because of the incline's increased steepness and possible frictional effects.
Normal Force in Inclined Planes
In an inclined plane, the normal force is not directed in the usual direction. Until now, normal force has always been seen to be directed upward in the opposite direction of gravity. The reality about normal forces is that they are always directed perpendicular to the surface the object is on, not always upward.
Components of Normal Force
In a normal plane, which is a horizontal surface, the object's weight is completely counteracted by the normal force.
N = mg
The normal force is perpendicular to the surface on an inclined plane, and it compensates the perpendicular component of the gravitational force.
if θ represents the angle of inclination, the normal force N can be expressed as:
N = mg cos(θ)
Example:
Imagine a book resting on a ramp. Gravity pulls the book straight down, but because the ramp is slanted, that pull isn't straight up against our hands. Here, gravity has got two faces. Gravity acts on the book with one big force, but on a slant, that force gets divided into two parts:
- Normal Force: This force pushes the book upward, perpendicular to the ramp's surface. Its like the ramp pushing back upward.
- Weight Pulling Down the Ramp: This force acts downward along the slope of the ramp it is the unbalanced force that pulls the book down
Gravity Force Components
There are two forces acting on the object, one object is broken down into a perpendicular components so that it can easily added to other forces acting on the object. The force acting on the object is broken down into two components - Horizontal and Vertical.
In inclined planes Concept, we resolve the Force vector (Fgrav) into two parts, one directed parallel to the inclined surface and the other directed perpendicular to the inclined surface.
On an inclined plane, the gravitational force can also be resolved into two components:
Fparallel = mgsin(θ){parallel to the incline}
Fperpendicular = mgcos(θ){perpendicular to the incline}
Object on an Inclined Plane
If an object of mass m is placed on a smooth inclined plane (i.e. frictional force F = 0) and released it will slide down the slope. To find the acceleration of the particle as it slides we resolve in the direction of motion.
F = ma
mg cos(90 — θ) = ma
g cos(90 — θ) = a
g sin(θ) = a
We can see that the particle's mass does not affect the acceleration but only the angle of the slope does.
If a particle of mass m is placed on a rough inclined plane (i.e. the frictional force F is not 0), if sliding of F is large enough.
We resolve perpendicular to the plane, where acceleration is zero.
F = ma,
R - mg cos θ = m×0
R = mg cos θ
We resolve in the direction of the slope, if the particle is at rest then
F = ma
mg cos(90 - θ) - F = m × 0
mg sin θ = F
Where F is the force of friction. We know that the maximum frictional force is given by Fmax = uR
Therefore
F ≤ uR
mg sin(θ) ≤ u mg cos(θ),
sin(θ)/cos(θ)=tan(θ)
tan(θ) ≤ u
Therefore the particle will remain at rest until tan(θ) > u, at this point it will accelerate down the slope.
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Solved Examples on Inclined Plane
Example 1: A block of mass 5 kg rests on an inclined plane inclined at an angle of 30 degrees to the horizontal. If the coefficient of friction between the block and the inclined plane is 0.2, calculate:
a) The normal force acting on the block.
b) The frictional force acting on the block if it is on the verge of sliding down.
c) The acceleration of the block if it is released from rest.
Solution:
a) The normal force (N) can be calculated using the formula:
N = mg cos(θ)
where m 5 kg, g =9.81 m/s (acceleration due to gravity), and θ = 30
N (5 kg)(9.81 m/s2) cos(30°)
N = (5)(9.81)(√3/2)
N = 42.73 N
b) The frictional force (f) can be calculated using the formula:
f = uN;
where u= 0.2 (coefficient of friction).
f = (0.2) (42.73)
f = 8.55 N
c) The net force acting on the block (Fnet) when it is released from rest is the component of the
gravitational force parallel to the inclined plane minus the frictional force:
Fnet = mg sin(θ) — f
Fnet = (5) (9.81) sin(30°) - 8.55
Fnet = 24.52 - 8.55
Fnet = 15.97 N
The acceleration (a) of the block can be calculated using Newton's second law (Fnet = ma)
15.97 = (5)a
a = 15.97/5
a = 3.194 m/s
Example 2: A 10 kg box is placed on an inclined plane inclined at an angle of 45 degrees to the horizontal. If the coefficient of friction between the box and the inclined plane is 0.3, determine the force parallel to the incline required to move the box up the incline at constant velocity.
Solution:
The force parallel to the incline required to move the box up the incline at constant velocity is
equal to the force of friction acting down the incline.
f=uN
Where u = 0.3 (coefficient of friction).
N = mg cos(θ)
N = (I0 kg)(9.81 m/s2) cos(45°)
N = 69.3N
f = 20.79 N
Example 3: A block of mass 12 kg is placed on an inclined plane inclined at an angle of 30 degrees to the horizontal. If the coefficient of friction between the block and the inclined plane is 0.25, calculate the acceleration of the block when it is released from rest.
Solution:
The net force acting on the block( net) when it is released from rest is the component of the
gravitational force parallel to the inclined plane
Fnet = mg sin(θ) — f
f = uN
N = mg cos(θ)
Fnet = mg sin(θ) — umg cos(θ)
Fnet =m(g sin(0) — ug cos(θ))
Fnet = 12(9.81 × sin(30°) - 0.25 × 9.81 × cos(30°))
Fnet = 12(4.905 - 0.25 × 8.484)
Fnet =12(4.905 - 2.121)
Fnet = 12 × 2.784
Fnet = 33.408 N
The acceleration (a) of the block can be calculated using Newton's second law (Fnet=m*a)
33.408 = 12 × a
a = 33.408/12
a = 2.784m s
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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