Page 1 Work And Energy Work: Work is the application of a force over a distance. Work is equal to the product of the force and the distance through which it produces movement. Although both force and displacement are vector quantities, having both magnitude and direction, work is a scalar quantity, having only magnitude. If the force acts in a direction other than that of the motion of the body, then only that component of the force in the direction of the motion produces work. If a force acts on a body constrained to remain stationary, no work is done by the force. Even if the body is in motion, the force must have a component in the direction of motion. WORK DONE BY A CONSTANT FORCE Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement W = F × s Thus, work done by force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Here the unit of work is Newton meter (N m) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Example: A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then work done is 5 N × 2 m =10 N m or 10 J. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement. Example: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage. Solution: Mass of luggage, m = 15 kg and Page 2 Work And Energy Work: Work is the application of a force over a distance. Work is equal to the product of the force and the distance through which it produces movement. Although both force and displacement are vector quantities, having both magnitude and direction, work is a scalar quantity, having only magnitude. If the force acts in a direction other than that of the motion of the body, then only that component of the force in the direction of the motion produces work. If a force acts on a body constrained to remain stationary, no work is done by the force. Even if the body is in motion, the force must have a component in the direction of motion. WORK DONE BY A CONSTANT FORCE Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement W = F × s Thus, work done by force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Here the unit of work is Newton meter (N m) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Example: A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then work done is 5 N × 2 m =10 N m or 10 J. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement. Example: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage. Solution: Mass of luggage, m = 15 kg and displacement, s = 1.5 m. Work done, W = F × s = mg × s = 15 kg × 10 m s -2 × 1.5 m = 225 kg m s -2 m = 225 N m = 225 J Work done is 225 J. Energy Energy is the power to change things. It is the ability to do work. It comes in different forms -- heat (thermal), light (radiant), mechanical, electrical, chemical, and nuclear energy. Energy is in everything. We use energy to do everything we do, from making a jump shot to baking our favorite cookies to sending astronauts into space -- energy is there, making sure we have the power to do it all. The unit of energy is the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J. FORMS OF ENERGY Energy is found in different forms, such as light, heat, sound and motion. There are many forms of energy, but they can all be put into two categories: kinetic and potential. Kinetic Energy Kinetic energy is motion––of waves, electrons, atoms, molecules, substances, and objects. Electrical Energy is the movement of electrical charges. Everything is made of tiny particles called atoms. Atoms are made of even smaller particles called electrons, protons, and neutrons. Applying a force can make some of the electrons move. Electrical charges moving through a wire is called electricity. Lightning is another example of electrical energy. Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Solar energy is an example of radiant energy. Page 3 Work And Energy Work: Work is the application of a force over a distance. Work is equal to the product of the force and the distance through which it produces movement. Although both force and displacement are vector quantities, having both magnitude and direction, work is a scalar quantity, having only magnitude. If the force acts in a direction other than that of the motion of the body, then only that component of the force in the direction of the motion produces work. If a force acts on a body constrained to remain stationary, no work is done by the force. Even if the body is in motion, the force must have a component in the direction of motion. WORK DONE BY A CONSTANT FORCE Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement W = F × s Thus, work done by force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Here the unit of work is Newton meter (N m) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Example: A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then work done is 5 N × 2 m =10 N m or 10 J. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement. Example: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage. Solution: Mass of luggage, m = 15 kg and displacement, s = 1.5 m. Work done, W = F × s = mg × s = 15 kg × 10 m s -2 × 1.5 m = 225 kg m s -2 m = 225 N m = 225 J Work done is 225 J. Energy Energy is the power to change things. It is the ability to do work. It comes in different forms -- heat (thermal), light (radiant), mechanical, electrical, chemical, and nuclear energy. Energy is in everything. We use energy to do everything we do, from making a jump shot to baking our favorite cookies to sending astronauts into space -- energy is there, making sure we have the power to do it all. The unit of energy is the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J. FORMS OF ENERGY Energy is found in different forms, such as light, heat, sound and motion. There are many forms of energy, but they can all be put into two categories: kinetic and potential. Kinetic Energy Kinetic energy is motion––of waves, electrons, atoms, molecules, substances, and objects. Electrical Energy is the movement of electrical charges. Everything is made of tiny particles called atoms. Atoms are made of even smaller particles called electrons, protons, and neutrons. Applying a force can make some of the electrons move. Electrical charges moving through a wire is called electricity. Lightning is another example of electrical energy. Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Solar energy is an example of radiant energy. Thermal Energy, or heat, is the internal energy in substances––the vibration and movement of the atoms and molecules within substances. Geothermal energy is an example of thermal energy. Motion Energy is the movement of objects and substances from one place to another. Objects and substances move when a force is applied according to Newton’s Laws of Motion. Wind is an example of motion energy. Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate––the energy is transferred through the substance in a wave. Potential Energy Potential energy is stored energy and the energy of position––gravitational energy. There are several forms of potential energy. Chemical Energy is energy stored in the bonds of atoms and molecules. It is the energy that holds these particles together. Biomass, petroleum, natural gas, and propane are examples of stored chemical energy. Stored Mechanical Energy is energy stored in objects by the application of a force. Compressed springs and stretched rubber bands are examples of stored mechanical energy. Nuclear Energy is energy stored in the nucleus of an atom––the energy that holds the nucleus together. The energy can be released when the nuclei are combined or split apart. Nuclear power plants split the nuclei of uranium atoms in a process called fission. The sun combines the nuclei of hydrogen atoms in a process called fusion. Scientists are working on creating fusion energy on earth, so that someday there might be fusion power plants. Gravitational Energy is the energy of position or place. A rock resting at the top of a hill contains gravitational potential energy. Hydropower, such as water in a reservoir behind a dam, is an example of gravitational potential energy. Let us express the kinetic energy of an object in the form of an equation. Consider an object of mass, m moving with a uniform velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it in the direction of its displacement. From Eq., the work done, W is F s. The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced. In section 8.5, we studied three equations of motion. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is v 2 – u 2 = 2as Page 4 Work And Energy Work: Work is the application of a force over a distance. Work is equal to the product of the force and the distance through which it produces movement. Although both force and displacement are vector quantities, having both magnitude and direction, work is a scalar quantity, having only magnitude. If the force acts in a direction other than that of the motion of the body, then only that component of the force in the direction of the motion produces work. If a force acts on a body constrained to remain stationary, no work is done by the force. Even if the body is in motion, the force must have a component in the direction of motion. WORK DONE BY A CONSTANT FORCE Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement W = F × s Thus, work done by force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Here the unit of work is Newton meter (N m) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Example: A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then work done is 5 N × 2 m =10 N m or 10 J. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement. Example: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage. Solution: Mass of luggage, m = 15 kg and displacement, s = 1.5 m. Work done, W = F × s = mg × s = 15 kg × 10 m s -2 × 1.5 m = 225 kg m s -2 m = 225 N m = 225 J Work done is 225 J. Energy Energy is the power to change things. It is the ability to do work. It comes in different forms -- heat (thermal), light (radiant), mechanical, electrical, chemical, and nuclear energy. Energy is in everything. We use energy to do everything we do, from making a jump shot to baking our favorite cookies to sending astronauts into space -- energy is there, making sure we have the power to do it all. The unit of energy is the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J. FORMS OF ENERGY Energy is found in different forms, such as light, heat, sound and motion. There are many forms of energy, but they can all be put into two categories: kinetic and potential. Kinetic Energy Kinetic energy is motion––of waves, electrons, atoms, molecules, substances, and objects. Electrical Energy is the movement of electrical charges. Everything is made of tiny particles called atoms. Atoms are made of even smaller particles called electrons, protons, and neutrons. Applying a force can make some of the electrons move. Electrical charges moving through a wire is called electricity. Lightning is another example of electrical energy. Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Solar energy is an example of radiant energy. Thermal Energy, or heat, is the internal energy in substances––the vibration and movement of the atoms and molecules within substances. Geothermal energy is an example of thermal energy. Motion Energy is the movement of objects and substances from one place to another. Objects and substances move when a force is applied according to Newton’s Laws of Motion. Wind is an example of motion energy. Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate––the energy is transferred through the substance in a wave. Potential Energy Potential energy is stored energy and the energy of position––gravitational energy. There are several forms of potential energy. Chemical Energy is energy stored in the bonds of atoms and molecules. It is the energy that holds these particles together. Biomass, petroleum, natural gas, and propane are examples of stored chemical energy. Stored Mechanical Energy is energy stored in objects by the application of a force. Compressed springs and stretched rubber bands are examples of stored mechanical energy. Nuclear Energy is energy stored in the nucleus of an atom––the energy that holds the nucleus together. The energy can be released when the nuclei are combined or split apart. Nuclear power plants split the nuclei of uranium atoms in a process called fission. The sun combines the nuclei of hydrogen atoms in a process called fusion. Scientists are working on creating fusion energy on earth, so that someday there might be fusion power plants. Gravitational Energy is the energy of position or place. A rock resting at the top of a hill contains gravitational potential energy. Hydropower, such as water in a reservoir behind a dam, is an example of gravitational potential energy. Let us express the kinetic energy of an object in the form of an equation. Consider an object of mass, m moving with a uniform velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it in the direction of its displacement. From Eq., the work done, W is F s. The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced. In section 8.5, we studied three equations of motion. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is v 2 – u 2 = 2as Or, We know F = m a. Thus, using in Eq., we can write the work done by the force, F as Or, W = ½ m {v² – u 2 } If the object is starting from its stationary position, that is, u = 0, then W = ½ mv 2 If u = 0, the work done will be ½ mv 2 Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is E k =½ mv 2 Example: An object of mass 15 kg is moving with a uniform velocity of 4 m s –1 . What is the kinetic energy possessed by the object? Solution: Mass of the object, m = 15 kg, velocity of the object, v = 4 m s –1 . E k =½ mv 2 =½× 15 kg × 4 m s –1 × 4 m s –1 = 120 J The kinetic energy of the object is 120 J. Example: What is the work to be done to increase the velocity of a car from 30 km h –1 to 60 km h –1 if the mass of the car is 1500 kg? Solution: Page 5 Work And Energy Work: Work is the application of a force over a distance. Work is equal to the product of the force and the distance through which it produces movement. Although both force and displacement are vector quantities, having both magnitude and direction, work is a scalar quantity, having only magnitude. If the force acts in a direction other than that of the motion of the body, then only that component of the force in the direction of the motion produces work. If a force acts on a body constrained to remain stationary, no work is done by the force. Even if the body is in motion, the force must have a component in the direction of motion. WORK DONE BY A CONSTANT FORCE Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement W = F × s Thus, work done by force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Here the unit of work is Newton meter (N m) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force. Example: A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement, then work done is 5 N × 2 m =10 N m or 10 J. Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement. Example: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage. Solution: Mass of luggage, m = 15 kg and displacement, s = 1.5 m. Work done, W = F × s = mg × s = 15 kg × 10 m s -2 × 1.5 m = 225 kg m s -2 m = 225 N m = 225 J Work done is 225 J. Energy Energy is the power to change things. It is the ability to do work. It comes in different forms -- heat (thermal), light (radiant), mechanical, electrical, chemical, and nuclear energy. Energy is in everything. We use energy to do everything we do, from making a jump shot to baking our favorite cookies to sending astronauts into space -- energy is there, making sure we have the power to do it all. The unit of energy is the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J. FORMS OF ENERGY Energy is found in different forms, such as light, heat, sound and motion. There are many forms of energy, but they can all be put into two categories: kinetic and potential. Kinetic Energy Kinetic energy is motion––of waves, electrons, atoms, molecules, substances, and objects. Electrical Energy is the movement of electrical charges. Everything is made of tiny particles called atoms. Atoms are made of even smaller particles called electrons, protons, and neutrons. Applying a force can make some of the electrons move. Electrical charges moving through a wire is called electricity. Lightning is another example of electrical energy. Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Solar energy is an example of radiant energy. Thermal Energy, or heat, is the internal energy in substances––the vibration and movement of the atoms and molecules within substances. Geothermal energy is an example of thermal energy. Motion Energy is the movement of objects and substances from one place to another. Objects and substances move when a force is applied according to Newton’s Laws of Motion. Wind is an example of motion energy. Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate––the energy is transferred through the substance in a wave. Potential Energy Potential energy is stored energy and the energy of position––gravitational energy. There are several forms of potential energy. Chemical Energy is energy stored in the bonds of atoms and molecules. It is the energy that holds these particles together. Biomass, petroleum, natural gas, and propane are examples of stored chemical energy. Stored Mechanical Energy is energy stored in objects by the application of a force. Compressed springs and stretched rubber bands are examples of stored mechanical energy. Nuclear Energy is energy stored in the nucleus of an atom––the energy that holds the nucleus together. The energy can be released when the nuclei are combined or split apart. Nuclear power plants split the nuclei of uranium atoms in a process called fission. The sun combines the nuclei of hydrogen atoms in a process called fusion. Scientists are working on creating fusion energy on earth, so that someday there might be fusion power plants. Gravitational Energy is the energy of position or place. A rock resting at the top of a hill contains gravitational potential energy. Hydropower, such as water in a reservoir behind a dam, is an example of gravitational potential energy. Let us express the kinetic energy of an object in the form of an equation. Consider an object of mass, m moving with a uniform velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it in the direction of its displacement. From Eq., the work done, W is F s. The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced. In section 8.5, we studied three equations of motion. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is v 2 – u 2 = 2as Or, We know F = m a. Thus, using in Eq., we can write the work done by the force, F as Or, W = ½ m {v² – u 2 } If the object is starting from its stationary position, that is, u = 0, then W = ½ mv 2 If u = 0, the work done will be ½ mv 2 Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is E k =½ mv 2 Example: An object of mass 15 kg is moving with a uniform velocity of 4 m s –1 . What is the kinetic energy possessed by the object? Solution: Mass of the object, m = 15 kg, velocity of the object, v = 4 m s –1 . E k =½ mv 2 =½× 15 kg × 4 m s –1 × 4 m s –1 = 120 J The kinetic energy of the object is 120 J. Example: What is the work to be done to increase the velocity of a car from 30 km h –1 to 60 km h –1 if the mass of the car is 1500 kg? Solution: Mass of the car, m =1500 kg, initial velocity of car, u = 30 km h -1 = 8.33 m s –1 . Similarly, the final velocity of the car, v = 60 km h –1 = 16.67 m s –1 . Therefore, the initial kinetic energy of the car, E kt =½ mu 2 =½ × 1500 kg × (8.33 m s –1 ) 2 = 52041.68 J. The final kinetic energy of the car, E kf =½ ×1500 kg × (16.67 m s –1 ) 2 = 208416.68 J. Thus, the work done = Change in kinetic energy = E kf - E kt = 156375 J. POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy. The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity. The potential energy of an object at a height depends on the ground level or the zero level you choose. An object in a given position can have a certain potential energy withRead More

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