Distance and Displacement
Distance and Displacement are two crucial terms that may seem the same but have different meanings and definitions.
Distance is a measure of “How much path is covered by an object in motion?” While Displacement is the measure of “How much path is covered by the object in a particular direction?”.
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- What is Displacement?
Displacement is defined as the total change - in the position of the object along with the direction of motion.
Displacement is known to be vector quantity. - As along with the magnitude of the changed
position, the direction of the motion is also taken into account. - Displacement can be positive, negative, or
zero.
Displacement is the shortest Path
Displacement here will be = 5
Difference between distance and displacement
Similarities Between Distance and Displacement
Despite a number of differences between them, both distance and displacement have quite similarities as well, some of them are listed below:
- The SI unit of both the Physical quantity is meter (m) only.
- Both distance and displacement require initial and final points for measurement.
- When the direction is not considered both are equal in magnitude, in most cases.
- Both have the same dimensions formula.
Distance and Displacement Solved Problems
1) John travels 150 miles
to North but then back-tracks to South for 65 miles to pick up a friend. What
is John’s total distance and displacement?Answer: John’s starting position Xi= 0.
Her final position Xf is the distance travelled N minus the
distance South.Calculating Displacement and Distance
Displacement = (150 mi N – 65 mi S)
Displacement = 85 miles N
Distance = 150+65 = 215 miles
2) An object moves along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.
a) Calculate the distance covered by the moving object.
b) Find the magnitude of the displacement of the object.
Solution
a) The distance covered by the moving object is calculated as follows:
AB + BC + CD + DE + EF
3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km
Frequently Asked Questions – FAQs
- Is this possible to have a negative distance?
- The distance can have only positive values and cannot be negative.
- Is displacement a scalar or vector quantity?
- Displacement is a vector quantity since it has both magnitude and direction.
- Can displacement be zero?
- Yes, displacement can be zero.
- What is meant by distance?
- Distance refers to the total movement of an object without any regard to direction.
- What is meant by displacement in simple term?
- Displacement is shortest distance between 2 points
- When do the Distance and Magnitude of Displacement become equal?
- The distance and the magnitude become equal when the motion is in a fixed direction or in one direction.
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Everything in this Universe is moving. The rate of movement of every object around you is different. Some may be moving very fast while others may be moving really slow. But a definite movement is visible in everything around us. But observe that we are living on planet earth which is constantly moving around the sun. The moon is moving around the earth, the Sun and Planets are moving around Galaxy. Light is moving from one place to another and even a tiny particle of an atom is constantly moving. Speed, Velocity and Acceleration are some basic terms in physics. Let us look one by one!
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What is Speed?
Speed defined as the rate of change of positon of an object in any direction
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The terms speed and velocity are often used to mean the same thing in everyday life but both are very different from each other.
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Speed is a scalar quantity, speed is the measurement of how fast or slow an object is moving, it can be measured into a numerical value
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Speed= Distance/ Time
Average Speed=Total
Distance Travelled/Total Time -
Here is the corrected version of the content with improved grammar:
What is Velocity?
Velocity is defined as the rate of change of displacement. It is the rate at which the object is changing its position. On the other hand, it is the direction in which the object is moving. Velocity is a vector quantity; it consists of both a numerical value and a direction.
The formula for velocity is given by:
Velocity = Change in distance / Change in time
For example, consider a car moving on the highway at the speed of 60 km/hr. At this particular time, if we only know the speed, we do not know the direction. However, if we specify that the car is moving at 60 km/hr in a northern direction, then its velocity is 60 km/hour north.
Negative and Positive Velocity
In the case of linear motion, take a ball as an example. As the ball exhibits 1D motion, a single axis (x-axis) can be used as the coordinate system to define its motion. If the ball travels along the positive x-axis, its velocity is positive, whereas if it travels along the negative x-axis, its velocity is negative.
When the ball moves along the positive x-axis (right), its velocity is positive, and when it moves along the negative x-axis (left), its velocity is negative.
Average Velocity
The average velocity is calculated as the total displacement divided by the total time:
Average velocity = Total Displacement\Total time
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What is Acceleration?
Acceleration is defined as the rate of change of velocity of an object with respect to time. It measures how much the velocity of an object changes at a specific point in time, typically within one second. Consequently, the velocity of a moving object can either increase or decrease over time.
Examples:
1. Imagine a bus moving at a speed of 40 km/hour north. The driver progressively accelerates, causing a change in velocity. This phenomenon is known as acceleration.
2. Consider riding a bicycle. Initially, you push the pedals rapidly, but after some time, you start pushing them more slowly. In this case, you are accelerating to decrease your speed, also known as deceleration.
The formula for acceleration is given by:
Acceleration} =Change in velocity/Change in time
Constant Acceleration:
When an object experiences a constant change in velocity over time, it is referred to as constant acceleration. For instance, if you throw a ball onto a slope, it will continuously move downward, increasing its velocity every second. In the first second, the velocity is 10 m/s, in the second second, it is 15 m/s, and in the third second, it reaches 20 m/s. This signifies a constant acceleration of 5 m/s.
It’s crucial to note that if an object maintains a consistent velocity, regardless of how fast it’s moving, it is not accelerating. Constant velocity implies zero acceleration.
Negative Acceleration or Deceleration:
When an object decreases its velocity, it is termed negative acceleration or deceleration. For instance, when you stop pushing the pedals on a bicycle, the tires gradually slow down, indicating negative acceleration. In this scenario, the velocity of the moving object keeps decreasing.
Difference Between Speed, Velocity and Acceleration
Difference between Speed and Velocity
Similarities Between Velocity and Aceleration
The Difference Between Speed and Velocity:
Speed is the rate of change of distance, indicating how much distance is covered in a particular time. On the other hand, velocity is the rate of change of displacement, signifying the change of distance in a specific direction with respect to time. Acceleration, meanwhile, is the rate of change of velocity per unit of time, representing an increase or decrease in velocity. Speed is a scalar quantity, while both velocity and acceleration are vector quantities.
A satellite’s original velocity is 15,000 m/s. After 60 seconds it s going 9,000 m/s. What is the acceleration?
Remember (final Velocity – initial Velocity) ÷ time is acceleration.
Final speed (velocity) = 9000 m/s
Initial speed (velocity) = 15,000 m/s
Time = 60 seconds
= (9000 m/s – 15,000 m/s) ÷ 60 s
= -6000 m/s ÷ 60 s
= -100 m/s2
This satellite is decelerating.
A roller coasters velocity at the top of the hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s. What is the acceleration of the coaster?
Remember (final Velocity – initial Velocity) ÷ time is acceleration.
Final speed (velocity) = 26 m/s
Initial speed (velocity) = 10 m/s
Time = 2 seconds
= (26m/s – 10m/s) ÷ 2 s
= 16 m/s ÷ 2s
= 8m/s2
a roller coaster accelerating 8m/s2
Work, Energy, and Power in Physics:
Work, energy, and power are fundamental concepts in physics. Work is considered to be done when a force, either a push or a pull, is applied to an object, resulting in a displacement of the object. The capacity to perform work is defined as energy, and power is the rate at which work is done per unit of time. This article delves into a detailed discussion of work, energy, and power.
What is Work?
Work is defined as a force acting upon an object to cause displacement. Alternatively, work is said to be done by a force on a body if the applied force causes the body to undergo a displacement. Certain conditions must be satisfied for work to be done:
1. A force must act on the body.
2. The body must be displaced from one position to another.
Work is influenced by two key factors:
1. Magnitude of force.
2. Direction in which the body moves due to the applied force.
The unit of work is measured by the product of displacement and force along with the direction of the force. It is a scalar quantity, and the SI unit of work is the Joule (J). The equation for work is given by:
Work} = F/d
Here,
F is the magnitude of the force applied,
d is the displacement of the body,
– The result is a scalar quantity representing work.
Calculation of Work with Displacement and Force:
If a body is displaced by d while a force F acts on it, the work(W) can be calculated using the formula:
W = Fd Cos(theta)(Angle between the displacement and force
Here, \(\theta\) is the angle between the displacement and the force. It’s important to note that work is done by a force when it produces motion in an object. For instance, if a person attempts to move a wall but the wall doesn’t move, no work is done because there is no displacement produced. However, energy is still expended as the person loses energy while attempting to push the wall, resulting in fatigue.
Work is only done when the applied force can change the direction of the object or move it.
Example of Work
Consider an object being horizontally dragged across the surface by a 200 N force acting parallel to the surface. The task is to find the amount of work done by the force in moving the object through a distance of 9 m.
Solution:
Given:
F = 200N d = 9m
Since F and d are in the same direction, (theta = 0) (where (theta) is the angle of the force to the direction of movement). Therefore,
W = Fd cos(theta)
W = 200 x 9 x cos(0)
W = 1800J ( since Cos0 =1)
Since the work done by the force in moving the object is 1800 Joules.
What is Energy?
Energy is the capacity to perform work. It is a scalar quantity, possessing only magnitude and no direction. The fundamental principle governing energy is the conservation of energy, stating that energy cannot be created nor destroyed; rather, it can only be transformed from one form to another. The unit of energy is the Joule (J), which is the same as that of work.
Energy manifests in various forms, leading to different types of energy. Two crucial types are kinetic energy and potential energy.
Kinetic Energy and Potential Energy:
1. Kinetic Energy (KE):
Kinetic energy is the energy associated with motion. It is calculated as the work required to accelerate an object of a given mass, distinguishing it from velocity. Once a body gains energy and undergoes acceleration, it maintains kinetic energy until its speed changes. The formula for kinetic energy is given by:
KE = 2mv^2
2. Potential Energy (PE):
Potential energy is the energy stored in an object and is quantified by the amount of work done. The potential energy of an object near the surface of the Earth is calculated using the formula:
PE = mgh
Where:
-m is the mass of the object,
– g is the acceleration due to gravity,
-h is the height above a reference point.
Unit of Energy:
The standard unit of energy is the Joule (J), named in honor of James Prescott Joule.
Other Types of Energy:
In addition to kinetic and potential energy, there are other significant types of energy, including:
1. Chemical Energy:
This type of energy is released during chemical reactions and is transformed into other substances.
2. Mechanical Energy:
Mechanical energy is the sum of potential energy and kinetic energy.
3. Electrical Energy:
Electrical energy arises from the movement between electrically charged particles.
Understanding these various forms of energy is crucial for comprehending the diverse ways in which energy is utilized and transformed in the natural world.
Magnetic Energy:
Magnetic energy is associated with the magnetic field generated by electric currents. It is the energy present in the form of electrons and is influenced by the properties of magnets and moving charges.
Nuclear Energy:
Nuclear energy is released during processes like fission or fusion, especially when harnessed for electricity generation. It originates from the immense energy stored within atomic nuclei.
Heat Energy:
Heat energy arises from the movement of atoms or molecules in solids, liquids, and gases. It is a result of the internal energy within a system and is often transferred through conduction, convection, or radiation.
Example: Kinetic and Potential Energy of a Thrown Ball:
Consider a ball with a mass of 2 kg thrown upward with a speed of 10 m/s. To find the kinetic and potential energy:
1. Kinetic Energy at the Time of Throwing:
Given m = 2 kg and u = 10 m/s, the kinetic energy can be calculated using the formula K = 1/2 m u^2
K =1/2 x2 x 10^2 = 100 J
2. Potential Energy at the Highest Point:
At the highest point, the entire kinetic energy is converted into potential energy. Therefore, potential energy at the highest point equals the initial kinetic energy:
Potential Energy = Initial Kinetic Energy= 100J
Example: Kinetic Energy of a Moving Car:
Consider a car with a mass of 500 kg moving with a velocity of 36 km/h. To find the kinetic energy and then calculate the kinetic energy if the velocity doubles:
1. Kinetic Energy at Initial Velocity
Given m = 500kg}and v = 36km/h}
K = 1/2 x 500x(10)^2 = 25,000 J
2.Kinetic Energy with Doubled Velocity:
When the velocity doubles v = 20, the new kinetic energy K is calculated as:
K = 1/2x 500 x(20)^2 = 100,000j= 100 KJ
Understanding kinetic and potential energy is essential for evaluating the dynamics and transformations of energy in various systems.
the kinetic energy K is calculated using K= 1/2 mv^2
What is Power?
Power is the measure of the rate at which work is done or the rate at which energy is transferred or converted, typically expressed in terms of time. Essentially, power signifies the amount of energy expended or converted per unit of time. A higher power value indicates a more rapid execution of work or energy transfer.
Formula of Power:
Power can be calculated by dividing the work done by the time taken, expressed by the formula:
P = W/t J
Where:
– P is the power,
– W is the work done,
– t is the time taken.
Example of Power:
Consider a garage hoist lifting a truck 3 meters above the ground in 15 seconds. Given the mass of the truck as 2000 kg, the power delivered to the truck can be calculated.
1. Calculate the Work Done:
First, find the force required to lift the truck against gravity:
F = mg = 2000 x 9.81 = 19620 N
Then, calculate the work done W using the formula W = Fd:
W = 19620 N x 3 m= 58860 Nm = 58860 J
2. Calculate the Power:
Finally, determine the power P using the formula P = W/t :
P = 58860 /15 = 3924 J/s = 3954W
Therefore, the power delivered to the truck is 3924 watts. This signifies the rate at which the garage hoist is doing work on the truck, lifting it against gravity.
Difference Between Speed, Velocity and Acceleration
Force and Momentum.
While force and momentum share similarities, there is a distinct difference between these physical quantities. Force typically refers to an external action, such as pushing or pulling, that causes a change in motion. On the other hand, momentum represents the amount of motion within a moving body. Let’s define each concept more explicitly.
Define Force:
Force is an external action that either pushes or pulls an object, resulting in a change in motion. It is a vector quantity, meaning it has both magnitude and direction. The direction of force is determined by the direction of acceleration. When an unstable force is applied to a body, it causes the object to move. However, when a stable force is applied, the object does not move, and its velocity remains zero. Mathematically, force is related to mass m and acceleration a through the equation F = ma
Types of Forces:
1. Contact Forces: These occur when two objects physically make contact. For example, a bat hitting a ball illustrates contact forces in action.
2. Forces Acting at a Distance: These forces act between objects without any physical contact.
Force can be further categorized based on its classification. For instance, in terms of work, a positive work done implies force acting in a positive direction, while negative work done indicates force in the opposite direction of motion.
Define Momentum:
Momentum is the measure of the amount of motion present in a moving object. It is a vector quantity, and its direction is determined by velocity. Momentum is affected by an unbalanced force acting on an object. The momentum of an object is given by the product of its mass m and velocity v : p = mv.
Key Points about Momentum:
– An increase in velocity leads to an increase in momentum.
– If two objects are moving at the same speed but have different masses, the momentum of the larger mass will be higher.
– The unit of momentum is kilograms per second (kg/s).
In summary, force and momentum are interconnected in the context of changes in motion. Force is the external action that causes such changes, while momentum quantifies the amount of motion present in a moving object.
Difference Between Force and Movementum
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How can we Change an Object’s Momentum to its Force Change an Object’s Momentum to its Force?
Force and momentum relation is given by the equation:
- F=dp/dt. The second law of motion gives the following equation as stated by Newton. The law states that the change in momentum of any object is given by mass into acceleration, that is, force.
- From the above equation, if the mass is constant, then, p=mv implies dp = mdv.
- ·Hence, the equation becomes F = m * dv/dt, which is equal to ma.
- Force and momentum relation can also be stated through the following equations:
- Momentum= (mass * velocity)
- As acceleration = velocity/time implies velocity = acceleration * time
- So, momentum= (mass * (acceleration * time))
- momentum = ((mass * acceleration) * time)
- momentum = force * time
- From the above equation, it is clear that momentum depends on time. It shows that as large a force is practiced on an object, the amount of momentum will increase. the increasing time, there will be a decrease in the amount of force if the momentum remains constant.
- Momentum and force both have magnitude as well as direction. It means both are vector quantities.
- If the velocity changes, then from the formula; p = mv;, momentum also changes. However, force changes only when the acceleration changes
Rest and Motion:
In our daily experiences, we encounter objects that are either in motion or at rest. These states of objects are fundamental concepts in physics. Let’s explore the definitions and examples of rest and motion.
Motion:
Motion is described as a change in an object’s position over time. When an object moves from one place to another, it is considered to be in a state of motion. Examples of motion include a moving bike, a rotating cycle wheel, a person walking on the footpath, the fluid motion of blood in veins and arteries, and even the lively activity of folk dancing.
Motion can be categorized into various types:
1. Translational Motion: An object moves along a path in any of the three dimensions.
– Example: A bike moving on a track or a person walking on the road.
2. Linear Motion: The body moves in a single direction along a single dimension.
3. Rotational Motion: An object moves along a circular path with a fixed axis.
– Example: Movement of the Earth on its axis or a bicycle moving on a circular track in a park.
4. Periodic Motion: A type of motion that repeats itself after certain intervals of time.
– Example: A bouncing ball or the vibrating tuning fork.
5. Simple Harmonic Motion: The motion of an object that moves to and fro about a mean position along a straight line.
– Example: The motion of a spring or the vibration of the eardrum.
6. Projectile Motion: Experienced by an object in the air under the influence of gravity.
– Example: Throwing a ball or a cannonball.
Rest:
Rest occurs when an object does not change its position with respect to time. Examples of objects at rest include a book kept on a table, benches in a park, or a person sitting on a chair.
Frame of Reference:
A frame of reference is a perspective from which an observer makes observations. For instance, a person standing on the moon might observe the Earth changing its position, while considering Earth as the frame of reference would imply that the object is at rest.
– Inertial Frame of Reference: If a frame of reference is not moving or moving with a constant velocity, it is termed an inertial frame of reference.
– Non-Inertial Frame of Reference: If a frame is accelerating or moving in a circular path with constant speed, it is termed a non-inertial frame of reference.
Laws of Motion:
Newton’s Laws of Motion lay the foundation for classical mechanics. These laws are universal and hold true in various scenarios:
1. First Law (Law of Inertia): A body at rest or in uniform motion will remain at rest or in uniform motion unless acted upon by a net external force.
– Example: A dropped ball continues falling.
2. Second Law (Law of Force and Acceleration): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. (F = ma).
– Example: It takes more effort to move a heavy box than a light one.
3. Third Law (Action and Reaction): For every action, there is an equal and opposite reaction.
– Example: If you push someone wearing roller skates, both you and the person move.
Understanding rest, motion, and the laws of motion is crucial for comprehending the dynamics of objects and their behavior in the physical world.
Summary
*FAQs:
1. Are rest and motion relative terms? Give an example.
– Yes, both rest and motion are relative terms, and they depend on the observer’s frame of reference. For instance, an observer may be at rest in their own frame of reference, but they could be in motion when viewed from another observer’s frame of reference.
2. Without any reference object, is it possible to mention whether an object is at rest or in motion?
– No, without any frame of reference or reference object, it is not possible to determine whether an object is at rest or in motion. For example, when traveling in a bus, to the passengers inside the bus, all other objects inside the bus may appear to be at rest relative to them, but an observer outside the bus may perceive both the bus and its contents to be in motion. The concept of rest or motion is relative to the chosen frame of reference.
Centripetal Force and Centrifugal Force: Two Sides of Circular Motion
Centripetal force and centrifugal force are closely related but operate in opposite directions, playing crucial roles in circular motion. According to Newton’s first law of motion, an object in motion tends to stay in motion in a straight line unless acted upon by an external force. However, when we experience circular motion, continuous acceleration implies the presence of external forces.
Centripetal Force:
Definition: Centripetal force is the force that keeps an object moving in a circular path and is always directed toward the center of that circle.
– Example: The gravitational force of the sun acting as a centripetal force keeps the Earth orbiting around it.
Centrifugal Force:
Definition: Centrifugal force is an apparent outward force on an object moving in a circle, making it feel as though it wants to move away from the center.
Example: The sensation experienced on a merry-go-round that seems to push you outward is an example of centrifugal force.
Key Differences:
1. Direction:
– Centripetal force points toward the center of the circle, acting as the centripetal force pulls an object inward.
– Centrifugal force appears to push outward, away from the center of the circle.
2. Nature:
– Centripetal force is a real force, such as tension, gravity, or friction, that acts on an object in circular motion.
– Centrifugal force is perceived and is not a real force but rather a result of inertia, the tendency of objects to move in a straight line.
3. Role:
– Centripetal force is responsible for keeping an object in circular motion and preventing it from moving in a straight line.
– Centrifugal force is an apparent force experienced by an object in circular motion, creating the sensation of being pushed outward.
In Summary Centripetal force acts as the inward force required for an object to move in a circle, while Centrifugal force is apparent outward force experienced by the object in circular motion. both force integral to understanding the dynamics of circular motion.
Difference between Centripetal force and Centrifugal force
FAQs:
1. Does centripetal force increase with speed?
– Yes! Centripetal force is given by the formula mv^2/R. This implies that as the speed (v) of the particle increases, the centripetal force experienced by it also increases.
2. Would gravity change if the Earth stopped spinning?
– If the Earth were to stop spinning suddenly, gravity would still exert its force, and we wouldn’t be thrown into space. Gravity continues to hold objects on the Earth’s surface even if the rotation ceases.
3. Does centrifugal force act inside or out?
– Centrifugal force acts outward. In circular motion, it is an apparent force that seems to push objects away from the center of rotation.