Conservative forces are those for which the work done on an object depends only upon the initial and final positions of the object, not on the route taken between them. That property guarantees that when an object is moved under the influence of a conservative force and returns to its original positRead more
Conservative forces are those for which the work done on an object depends only upon the initial and final positions of the object, not on the route taken between them. That property guarantees that when an object is moved under the influence of a conservative force and returns to its original position, the total work done by the force is zero.
One of the most important characteristics of conservative forces is that they are associated with potential energy. When an object moves in a conservative force field, its potential energy changes, and this change is equal to the work done by the force. Thus, for example, in the gravitational field, when an object is lifted, it gains potential energy equal to the work done against gravity.
In addition, conservative forces are necessary in the principle of energy conservation. The total mechanical energy—potential and kinetic energy—is conserved in systems affected by these forces. Energy can be transformed from potential to kinetic form and vice versa; however, its total is kept constant.
Examples of conservative forces include gravitational force, electrostatic force, and spring force. These forces are fundamental in classical mechanics, explaining various physical phenomena and the behavior of systems in motion and energy transfer.
To derive the kinetic energy expression, we begin with the work-energy relationship. The work-energy principle states that work done on an object is equal to the change in its kinetic energy. Work done when a force acts on an object can be expressed as force times distance, causing the body to moveRead more
To derive the kinetic energy expression, we begin with the work-energy relationship. The work-energy principle states that work done on an object is equal to the change in its kinetic energy. Work done when a force acts on an object can be expressed as force times distance, causing the body to move some distance in the direction of the applied force.
By Newton’s second law, force is defined as the product of mass and acceleration. If a body has acceleration, there is a change in its velocity. If the body starts from rest and the acceleration is uniform, its final velocity is determined by the distance and the acceleration of the body.
Putting the definition of force and distance into the equation for work done, we arrive at the work done on the object being related to its mass and the square of its velocity. The work done to accelerate an object from rest to some velocity goes directly into its kinetic energy.
Therefore, kinetic energy is defined as the energy an object has due to its motion, dependent on its mass and the square of its velocity. Therein, the interrelation of both mass and speed shows how important those values are in establishing the energy belonging to moving objects.
Kinetic energy is the energy an object has due to its motion. It depends on two main things: the mass of the object and the velocity at which the object moves. In other words, the more massive an object is or the greater the velocity, the higher the kinetic energy. This sort of energy is a scalar quRead more
Kinetic energy is the energy an object has due to its motion. It depends on two main things: the mass of the object and the velocity at which the object moves. In other words, the more massive an object is or the greater the velocity, the higher the kinetic energy. This sort of energy is a scalar quantity—a value with magnitude but no direction.
There are many examples of kinetic energy in real life: for example, a moving car, which increases in kinetic energy as the speed increases or even as the mass of the object increases. Therefore, a truck moving at a speed similar to that of a bicycle holds more kinetic energy due to its increased mass. In sports, when a soccer player kicks a ball, there is kinetic energy in the ball as it moves, which affects its speed and direction.
Flowing water in rivers holds kinetic energy that can be used in hydroelectric power. An airplane in flight contains plenty of kinetic energy, which is needed to maintain lift and propulsion. Even running animals—such as dogs in a park—are examples of kinetic energy, as they move fast.
In a nutshell, kinetic energy lies at the basis of several physical phenomena, apparently experienced in everyday situations, and this forms one of the core ideas regarding motion and the transfer of energies.
Einstein's mass-energy equivalence shows that mass and energy are inextricably linked and interchangeable. This means that a small quantity of mass can be converted into a huge amount of energy because the speed of light squared is very large. That was the revolutionary idea that transformed our perRead more
Einstein’s mass-energy equivalence shows that mass and energy are inextricably linked and interchangeable. This means that a small quantity of mass can be converted into a huge amount of energy because the speed of light squared is very large. That was the revolutionary idea that transformed our perception of physics, since it showed that mass could be interpreted as some sort of stored energy.
Practical applications of mass-energy equivalence include:
1. Nuclear Energy: A very small amount of mass gets converted to energy in nuclear reactions like fission and fusion. This powers nuclear reactors and accounts for the explosive energy released by atomic bombs.
2. Medical Applications: Many techniques, such as Positron Emission Tomography (PET) scans, depend on mass-energy equivalence. In a PET scan, positrons (the antimatter equivalent of electrons) annihilate with electrons to produce gamma rays that form images of metabolic activity in the body.
3. Particle Physics: In high-energy particle colliders, particles are accelerated to nearly the speed of light. When these particles collide, mass can be converted into energy, helping scientists discover new particles and understand fundamental forces.
4. Astrophysics: The principle can be applied to explain processes in stars, whereby nuclear fusion changes hydrogen into helium, releasing enormous energy that powers stars like the Sun.
Einstein’s mass-energy equivalence has had a tremendous impact across different fields, shaping energy production, medical imaging, and fundamental research in physics.
To prove that gravitational force is conservative, we would need to show that the work done by this force in moving any object between two points is path-independent. The work depends only on the initial and final positions of the object. Gravitational force is exerted on an object by the mass of thRead more
To prove that gravitational force is conservative, we would need to show that the work done by this force in moving any object between two points is path-independent. The work depends only on the initial and final positions of the object.
Gravitational force is exerted on an object by the mass of the Earth, pulling it toward the center. In the case of vertical motion, the work done by gravity can be understood in terms of a change in height. If an object moves from a higher to a lower position, gravity does positive work; from a low to a high position, the work done by gravity is negative, since gravity opposes the motion.
This work can be interpreted in terms of potential energy associated with the object’s height. As the object moves, its gravitational potential energy changes, reflecting the work done by gravity. The important point is that the work done depends only on the difference in heights between the starting and ending points, not on the path taken.
Since the work done by gravitational force is path-independent, and we can associate this work with a potential energy function, we conclude that gravitational force must be conservative. This has very important implications in many fields, from mechanics to energy conservation.
What are conservative forces? Explains
Conservative forces are those for which the work done on an object depends only upon the initial and final positions of the object, not on the route taken between them. That property guarantees that when an object is moved under the influence of a conservative force and returns to its original positRead more
Conservative forces are those for which the work done on an object depends only upon the initial and final positions of the object, not on the route taken between them. That property guarantees that when an object is moved under the influence of a conservative force and returns to its original position, the total work done by the force is zero.
One of the most important characteristics of conservative forces is that they are associated with potential energy. When an object moves in a conservative force field, its potential energy changes, and this change is equal to the work done by the force. Thus, for example, in the gravitational field, when an object is lifted, it gains potential energy equal to the work done against gravity.
In addition, conservative forces are necessary in the principle of energy conservation. The total mechanical energy—potential and kinetic energy—is conserved in systems affected by these forces. Energy can be transformed from potential to kinetic form and vice versa; however, its total is kept constant.
Examples of conservative forces include gravitational force, electrostatic force, and spring force. These forces are fundamental in classical mechanics, explaining various physical phenomena and the behavior of systems in motion and energy transfer.
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Derive an expression for the kinetic energy of a body of mass m moving with velocity v.
To derive the kinetic energy expression, we begin with the work-energy relationship. The work-energy principle states that work done on an object is equal to the change in its kinetic energy. Work done when a force acts on an object can be expressed as force times distance, causing the body to moveRead more
To derive the kinetic energy expression, we begin with the work-energy relationship. The work-energy principle states that work done on an object is equal to the change in its kinetic energy. Work done when a force acts on an object can be expressed as force times distance, causing the body to move some distance in the direction of the applied force.
By Newton’s second law, force is defined as the product of mass and acceleration. If a body has acceleration, there is a change in its velocity. If the body starts from rest and the acceleration is uniform, its final velocity is determined by the distance and the acceleration of the body.
Putting the definition of force and distance into the equation for work done, we arrive at the work done on the object being related to its mass and the square of its velocity. The work done to accelerate an object from rest to some velocity goes directly into its kinetic energy.
Therefore, kinetic energy is defined as the energy an object has due to its motion, dependent on its mass and the square of its velocity. Therein, the interrelation of both mass and speed shows how important those values are in establishing the energy belonging to moving objects.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/
What is kinetic energy? Give some examples.
Kinetic energy is the energy an object has due to its motion. It depends on two main things: the mass of the object and the velocity at which the object moves. In other words, the more massive an object is or the greater the velocity, the higher the kinetic energy. This sort of energy is a scalar quRead more
Kinetic energy is the energy an object has due to its motion. It depends on two main things: the mass of the object and the velocity at which the object moves. In other words, the more massive an object is or the greater the velocity, the higher the kinetic energy. This sort of energy is a scalar quantity—a value with magnitude but no direction.
There are many examples of kinetic energy in real life: for example, a moving car, which increases in kinetic energy as the speed increases or even as the mass of the object increases. Therefore, a truck moving at a speed similar to that of a bicycle holds more kinetic energy due to its increased mass. In sports, when a soccer player kicks a ball, there is kinetic energy in the ball as it moves, which affects its speed and direction.
Flowing water in rivers holds kinetic energy that can be used in hydroelectric power. An airplane in flight contains plenty of kinetic energy, which is needed to maintain lift and propulsion. Even running animals—such as dogs in a park—are examples of kinetic energy, as they move fast.
In a nutshell, kinetic energy lies at the basis of several physical phenomena, apparently experienced in everyday situations, and this forms one of the core ideas regarding motion and the transfer of energies.
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/
What is Einstein’s mass-energy equivalence? Mention some of its practical applications.
Einstein's mass-energy equivalence shows that mass and energy are inextricably linked and interchangeable. This means that a small quantity of mass can be converted into a huge amount of energy because the speed of light squared is very large. That was the revolutionary idea that transformed our perRead more
Einstein’s mass-energy equivalence shows that mass and energy are inextricably linked and interchangeable. This means that a small quantity of mass can be converted into a huge amount of energy because the speed of light squared is very large. That was the revolutionary idea that transformed our perception of physics, since it showed that mass could be interpreted as some sort of stored energy.
Practical applications of mass-energy equivalence include:
1. Nuclear Energy: A very small amount of mass gets converted to energy in nuclear reactions like fission and fusion. This powers nuclear reactors and accounts for the explosive energy released by atomic bombs.
2. Medical Applications: Many techniques, such as Positron Emission Tomography (PET) scans, depend on mass-energy equivalence. In a PET scan, positrons (the antimatter equivalent of electrons) annihilate with electrons to produce gamma rays that form images of metabolic activity in the body.
3. Particle Physics: In high-energy particle colliders, particles are accelerated to nearly the speed of light. When these particles collide, mass can be converted into energy, helping scientists discover new particles and understand fundamental forces.
4. Astrophysics: The principle can be applied to explain processes in stars, whereby nuclear fusion changes hydrogen into helium, releasing enormous energy that powers stars like the Sun.
Einstein’s mass-energy equivalence has had a tremendous impact across different fields, shaping energy production, medical imaging, and fundamental research in physics.
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/
Show analytically that gravitational force is a conservative force.
To prove that gravitational force is conservative, we would need to show that the work done by this force in moving any object between two points is path-independent. The work depends only on the initial and final positions of the object. Gravitational force is exerted on an object by the mass of thRead more
To prove that gravitational force is conservative, we would need to show that the work done by this force in moving any object between two points is path-independent. The work depends only on the initial and final positions of the object.
Gravitational force is exerted on an object by the mass of the Earth, pulling it toward the center. In the case of vertical motion, the work done by gravity can be understood in terms of a change in height. If an object moves from a higher to a lower position, gravity does positive work; from a low to a high position, the work done by gravity is negative, since gravity opposes the motion.
This work can be interpreted in terms of potential energy associated with the object’s height. As the object moves, its gravitational potential energy changes, reflecting the work done by gravity. The important point is that the work done depends only on the difference in heights between the starting and ending points, not on the path taken.
Since the work done by gravitational force is path-independent, and we can associate this work with a potential energy function, we conclude that gravitational force must be conservative. This has very important implications in many fields, from mechanics to energy conservation.
For more content :
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/