When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the saRead more
When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the same speed of the original velocity of the body.
In this case, if one part traces its trajectory with the same speed, we must calculate the velocity of the second part. Since momentum is conserved everywhere, the total momentum before and after the break will be the same.
In that case, one part moving in the opposite direction with the same speed gives a negative contribution to the total momentum of the system. The other portion must make up for this alteration in order to ensure that the sum of the momentums remains unchanged. By the law of conservation of momentum, it is apparent that the second portion has to move in the forward direction at a greater velocity. More precisely, its velocity will be three times the original velocity of the body before it broke up. This shows how motion and the conservation principles are interrelated in physics. Finally, the second part of the body moves with a velocity three times greater than that of the original body.
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulumRead more
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulum bob at point Q after losing 10% of its energy due to air resistance, we begin with understanding the system.
However, during this process, the pendulum loses 10% of its total mechanical energy to air resistance. Thus, only 90% of the initial total energy is available for conversion into kinetic energy at point Q. The energy conversion results in the pendulum bob gaining speed as it moves downward.
We can calculate the velocity at point Q. The lost energy is the one that reduces the kinetic energy the bob can have at the lowest point. The remaining energy translates into kinetic energy, which can be expressed in terms of the mass of the bob and its velocity.
Ultimately, taking into consideration the energy transformations and the energy loss effect we observe that the pendulum bob at point Q will have a velocity of 6 meters per second. The answer is, therefore, 6 m/s.
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2Read more
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2 cm results in a total stretch of 4 cm.
The energy stored in the spring at any stretch can be expressed as follows:
1. For the first stretch of 2 cm:
Energy = k ⋅ (2²) = k ⋅ 4 (where k is the spring constant)
2. For the total stretch of 4 cm:
Energy = k ⋅ (4²) = k ⋅ 16
The increase in energy when stretched from 2 cm to 4 cm can be calculated as follows:
– Total energy at 4 cm: k .16
– Initial energy at 2 cm: k . 4
The increase in energy will then be:
– Increase in energy = k . 16 – k . 4 = k . 12
Given that k⋅4 = 100 J, we know that the total energy stored at 4 cm is 4⋅ 100 = 400 J.
Hence, the amount of increase in the energy stored when the spring is stretched further by 2 cm is: 300 J.
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principlesRead more
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principles from the law of conservation of momentum and that relating mass with kinetic energy.
In a system in which two objects collide or separate, the total momentum before and after the event is constant provided no external forces act on them. In this case, because the bomb was stationary before it exploded, the total momentum was zero, so the momentum of the fragments has to balance out after the explosion.
We know that the kinetic energy is distributed between the two fragments based on their respective masses, as deduced from the mass ratio of the fragments. The smaller fragment will have a proportionately smaller amount of kinetic energy compared to the larger fragment. Therefore, we can say that the kinetic energy of the smaller part will be 48,000 joules, and that of the larger part is going to be the rest after the explosion. Such a process explains how the principles of mass, momentum, and kinetic energy work hand in hand in an explosion.
When the kinetic energy of a body is increased, this affects the body's momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quRead more
When the kinetic energy of a body is increased, this affects the body’s momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quantity alters the other.
If the kinetic energy of a body becomes four times its initial value, then its momentum will double. This result follows from the mathematical relationship between kinetic energy and momentum. Kinetic energy increases with the square of velocity, but momentum increases linearly with velocity. Thus, when kinetic energy is multiplied by a factor of four, the velocity of the body increases by a factor of two, and momentum, being directly proportional to velocity, also doubles. For instance, let us consider a moving body whose kinetic energy is quadrupled by some external influence, such as an applied force. Its velocity will increase by the square root of four, that is, two, leading to a doubling of its momentum. This relationship shows how energy and motion are linked and how an increase in energy directly impacts the momentum of the body in a predictable way.
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions. KineRead more
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions.
Kinetic energy, however, is not conserved. It is conserved only in elastic collisions, where there is no loss of energy to heat, sound, or deformation. In such cases, the total kinetic energy of the system before and after the collision remains the same. Elastic collisions typically occur at a microscopic level, such as between gas particles, where energy is perfectly transferred between colliding objects.
In inelastic collisions, kinetic energy is not conserved. A part of it is converted into other forms of energy, such as heat, sound, or potential energy due to deformation of the colliding objects. Inelastic collisions are very common in everyday life, like a car crash, where deformation of the vehicles and heat generation result in loss of kinetic energy.
Thus, momentum conservation is a universal law of all collisions, whereas the former depends on the nature of the collision and points out to be an important distinction between the two.
To solve the problem of calculating work done in stretching a spring, we must refer to the property of the spring as described in Hooke's Law. In this law, it is defined that the amount of force applied to stretch the spring is proportional to the stretching from its original length. The force increRead more
To solve the problem of calculating work done in stretching a spring, we must refer to the property of the spring as described in Hooke’s Law. In this law, it is defined that the amount of force applied to stretch the spring is proportional to the stretching from its original length. The force increases linearly with the degree of stretching the spring. The work done in stretching the spring is equivalent to the energy stored in it, often referred to as elastic potential energy.
The work done is visualized to be the area under a graph of force extension. Since this relationship between the force and extension is linear, the graph plots as a triangle. The extension of the spring is represented by the base of this triangle, while the height would represent the maximum force required. Therefore, work done is directly proportional to the square of extension.
In this given case, the spring would need a force of 10 N for every millimeter of extension, and it is stretched 40 mm. When we use the formula for work done in a spring, substituting the given values enables us to calculate how much energy is in the spring due to this extension. When using the result of this computation, we obtain a total work done of 8 J, meaning it amounts to the amount of energy required to extend the spring by 40 mm.
A 3.0 kg bomb explodes in mid-air, breaking into two pieces of mass 2.0 kg and 1.0 kg. The smaller piece, with mass 1.0 kg, is ejected at a speed of 89 m/s. We want to find the total energy transferred to the two pieces. First, we will calculate the kinetic energy of the smaller piece. The kinetic eRead more
A 3.0 kg bomb explodes in mid-air, breaking into two pieces of mass 2.0 kg and 1.0 kg. The smaller piece, with mass 1.0 kg, is ejected at a speed of 89 m/s. We want to find the total energy transferred to the two pieces. First, we will calculate the kinetic energy of the smaller piece. The kinetic energy depends on the mass and the square of the speed of the fragment. We apply the principle of conservation of momentum to find the speed of the larger fragment. Since the total momentum before the explosion is zero, the momentum after the explosion must also equal zero. So, by studying the masses and velocities, we can deduce the speed of the 2.0 kg fragment.
After calculating the kinetic energy of each fragment, these values are combined to find total energy imparted during the explosion. The calculated total energy expresses the amount of energy released from the explosion, which is equally distributed between two fragments. Hence, the answer shows the quantity of energy transmitted to the fragments, which remains a significant requirement in the domain of physics as an understanding related to the mechanics of explosions.
When a particle with mass m₁ is moving at a certain velocity, it collides with another particle that is at rest and has mass m₂. Upon collision, the two masses become embedded in one another to form a single composite object. The collision process is important in understanding the principles of momeRead more
When a particle with mass m₁ is moving at a certain velocity, it collides with another particle that is at rest and has mass m₂. Upon collision, the two masses become embedded in one another to form a single composite object. The collision process is important in understanding the principles of momentum and energy transfer.
Before the collision, the moving mass has kinetic energy because it is moving. The stationary mass does not have any kinetic energy because it is not moving. After collision, the two masses exert forces on each other and thus momentum is transferred from one to another. By the principle of conservation of momentum, the total momentum of the system before the collision must be equal to the total momentum after the collision.
On the other hand, the combined velocity after embedding will be smaller than that before collision due to the embedding of two masses together. Here again, during a collision, kinetic energy changes partly into heat and sound energies and other forms, thereby causing the system velocity to drop at the collision time, reflecting complex dynamics during an inelastic collision.
To determine the potential energy loss of a 20 kg ball dropped from 50 cm height, we shall use the potential energy formula: Potential Energy = mass × gravitational acceleration × height Mass (m) = 20 kg Height (h) = 50 cm = 0.5 m Gravitational acceleration (g) ≈ 9.8 m/s² Putting all these values inRead more
To determine the potential energy loss of a 20 kg ball dropped from 50 cm height, we shall use the potential energy formula:
Potential Energy = mass × gravitational acceleration × height
Mass (m) = 20 kg
Height (h) = 50 cm = 0.5 m
Gravitational acceleration (g) ≈ 9.8 m/s²
Putting all these values into the formula,
Potential Energy = 20 kg × 9.8 m/s² × 0.5 m
Potential Energy = 20 kg × 4.9 m²/s²
Potential Energy = 98 J
This implies that the potential energy of the ball has decreased by 98 J.
A body moving with a velocity v, breaks up into two equal parts. One of the parts retraces back with velocity v, Then the velocity of the other part is
When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the saRead more
When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the same speed of the original velocity of the body.
In this case, if one part traces its trajectory with the same speed, we must calculate the velocity of the second part. Since momentum is conserved everywhere, the total momentum before and after the break will be the same.
In that case, one part moving in the opposite direction with the same speed gives a negative contribution to the total momentum of the system. The other portion must make up for this alteration in order to ensure that the sum of the momentums remains unchanged. By the law of conservation of momentum, it is apparent that the second portion has to move in the forward direction at a greater velocity. More precisely, its velocity will be three times the original velocity of the body before it broke up. This shows how motion and the conservation principles are interrelated in physics. Finally, the second part of the body moves with a velocity three times greater than that of the original body.
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The bob of a pendulum of length 2 m lies at P. When it reaches Q, it loses 10 % of its total energy due to air resistance. The velocity at Q is
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulumRead more
We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulum bob at point Q after losing 10% of its energy due to air resistance, we begin with understanding the system.
However, during this process, the pendulum loses 10% of its total mechanical energy to air resistance. Thus, only 90% of the initial total energy is available for conversion into kinetic energy at point Q. The energy conversion results in the pendulum bob gaining speed as it moves downward.
We can calculate the velocity at point Q. The lost energy is the one that reduces the kinetic energy the bob can have at the lowest point. The remaining energy translates into kinetic energy, which can be expressed in terms of the mass of the bob and its velocity.
Ultimately, taking into consideration the energy transformations and the energy loss effect we observe that the pendulum bob at point Q will have a velocity of 6 meters per second. The answer is, therefore, 6 m/s.
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When a spring is stretched by 2 cm, it stores 100J of energy. If it is stretched further by 2 cm, the stored energy will be increased by
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2Read more
When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2 cm results in a total stretch of 4 cm.
The energy stored in the spring at any stretch can be expressed as follows:
1. For the first stretch of 2 cm:
Energy = k ⋅ (2²) = k ⋅ 4 (where k is the spring constant)
2. For the total stretch of 4 cm:
Energy = k ⋅ (4²) = k ⋅ 16
The increase in energy when stretched from 2 cm to 4 cm can be calculated as follows:
– Total energy at 4 cm: k .16
– Initial energy at 2 cm: k . 4
The increase in energy will then be:
– Increase in energy = k . 16 – k . 4 = k . 12
Given that k⋅4 = 100 J, we know that the total energy stored at 4 cm is 4⋅ 100 = 400 J.
Hence, the amount of increase in the energy stored when the spring is stretched further by 2 cm is: 300 J.
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A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. The total K.E. of the fragments is 6.4 x 10⁴ J. What is the K.E. of the smaller fragment?
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principlesRead more
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principles from the law of conservation of momentum and that relating mass with kinetic energy.
In a system in which two objects collide or separate, the total momentum before and after the event is constant provided no external forces act on them. In this case, because the bomb was stationary before it exploded, the total momentum was zero, so the momentum of the fragments has to balance out after the explosion.
We know that the kinetic energy is distributed between the two fragments based on their respective masses, as deduced from the mass ratio of the fragments. The smaller fragment will have a proportionately smaller amount of kinetic energy compared to the larger fragment. Therefore, we can say that the kinetic energy of the smaller part will be 48,000 joules, and that of the larger part is going to be the rest after the explosion. Such a process explains how the principles of mass, momentum, and kinetic energy work hand in hand in an explosion.
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If the kinetic energy of a body becomes four times of its initial value, then new momentum will
When the kinetic energy of a body is increased, this affects the body's momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quRead more
When the kinetic energy of a body is increased, this affects the body’s momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quantity alters the other.
If the kinetic energy of a body becomes four times its initial value, then its momentum will double. This result follows from the mathematical relationship between kinetic energy and momentum. Kinetic energy increases with the square of velocity, but momentum increases linearly with velocity. Thus, when kinetic energy is multiplied by a factor of four, the velocity of the body increases by a factor of two, and momentum, being directly proportional to velocity, also doubles. For instance, let us consider a moving body whose kinetic energy is quadrupled by some external influence, such as an applied force. Its velocity will increase by the square root of four, that is, two, leading to a doubling of its momentum. This relationship shows how energy and motion are linked and how an increase in energy directly impacts the momentum of the body in a predictable way.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/
Which of the following is true?
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions. KineRead more
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions.
Kinetic energy, however, is not conserved. It is conserved only in elastic collisions, where there is no loss of energy to heat, sound, or deformation. In such cases, the total kinetic energy of the system before and after the collision remains the same. Elastic collisions typically occur at a microscopic level, such as between gas particles, where energy is perfectly transferred between colliding objects.
In inelastic collisions, kinetic energy is not conserved. A part of it is converted into other forms of energy, such as heat, sound, or potential energy due to deformation of the colliding objects. Inelastic collisions are very common in everyday life, like a car crash, where deformation of the vehicles and heat generation result in loss of kinetic energy.
Thus, momentum conservation is a universal law of all collisions, whereas the former depends on the nature of the collision and points out to be an important distinction between the two.
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A spring 40 mm long is stretched by the application of a force. If 10 N force is required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is
To solve the problem of calculating work done in stretching a spring, we must refer to the property of the spring as described in Hooke's Law. In this law, it is defined that the amount of force applied to stretch the spring is proportional to the stretching from its original length. The force increRead more
To solve the problem of calculating work done in stretching a spring, we must refer to the property of the spring as described in Hooke’s Law. In this law, it is defined that the amount of force applied to stretch the spring is proportional to the stretching from its original length. The force increases linearly with the degree of stretching the spring. The work done in stretching the spring is equivalent to the energy stored in it, often referred to as elastic potential energy.
The work done is visualized to be the area under a graph of force extension. Since this relationship between the force and extension is linear, the graph plots as a triangle. The extension of the spring is represented by the base of this triangle, while the height would represent the maximum force required. Therefore, work done is directly proportional to the square of extension.
In this given case, the spring would need a force of 10 N for every millimeter of extension, and it is stretched 40 mm. When we use the formula for work done in a spring, substituting the given values enables us to calculate how much energy is in the spring due to this extension. When using the result of this computation, we obtain a total work done of 8 J, meaning it amounts to the amount of energy required to extend the spring by 40 mm.
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A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 89 ms⁻¹ . The total energy imparted to the two fragments is
A 3.0 kg bomb explodes in mid-air, breaking into two pieces of mass 2.0 kg and 1.0 kg. The smaller piece, with mass 1.0 kg, is ejected at a speed of 89 m/s. We want to find the total energy transferred to the two pieces. First, we will calculate the kinetic energy of the smaller piece. The kinetic eRead more
A 3.0 kg bomb explodes in mid-air, breaking into two pieces of mass 2.0 kg and 1.0 kg. The smaller piece, with mass 1.0 kg, is ejected at a speed of 89 m/s. We want to find the total energy transferred to the two pieces. First, we will calculate the kinetic energy of the smaller piece. The kinetic energy depends on the mass and the square of the speed of the fragment. We apply the principle of conservation of momentum to find the speed of the larger fragment. Since the total momentum before the explosion is zero, the momentum after the explosion must also equal zero. So, by studying the masses and velocities, we can deduce the speed of the 2.0 kg fragment.
After calculating the kinetic energy of each fragment, these values are combined to find total energy imparted during the explosion. The calculated total energy expresses the amount of energy released from the explosion, which is equally distributed between two fragments. Hence, the answer shows the quantity of energy transmitted to the fragments, which remains a significant requirement in the domain of physics as an understanding related to the mechanics of explosions.
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A particle of mass m₁ moving with velocity v collides with a mass m₂ at rest, then they get embedded. At the instant of collision, velocity of the system
When a particle with mass m₁ is moving at a certain velocity, it collides with another particle that is at rest and has mass m₂. Upon collision, the two masses become embedded in one another to form a single composite object. The collision process is important in understanding the principles of momeRead more
When a particle with mass m₁ is moving at a certain velocity, it collides with another particle that is at rest and has mass m₂. Upon collision, the two masses become embedded in one another to form a single composite object. The collision process is important in understanding the principles of momentum and energy transfer.
Before the collision, the moving mass has kinetic energy because it is moving. The stationary mass does not have any kinetic energy because it is not moving. After collision, the two masses exert forces on each other and thus momentum is transferred from one to another. By the principle of conservation of momentum, the total momentum of the system before the collision must be equal to the total momentum after the collision.
On the other hand, the combined velocity after embedding will be smaller than that before collision due to the embedding of two masses together. Here again, during a collision, kinetic energy changes partly into heat and sound energies and other forms, thereby causing the system velocity to drop at the collision time, reflecting complex dynamics during an inelastic collision.
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The decrease in the potential energy of a ball of mass 20 kg, which falls from a height 50 cm is
To determine the potential energy loss of a 20 kg ball dropped from 50 cm height, we shall use the potential energy formula: Potential Energy = mass × gravitational acceleration × height Mass (m) = 20 kg Height (h) = 50 cm = 0.5 m Gravitational acceleration (g) ≈ 9.8 m/s² Putting all these values inRead more
To determine the potential energy loss of a 20 kg ball dropped from 50 cm height, we shall use the potential energy formula:
Potential Energy = mass × gravitational acceleration × height
Mass (m) = 20 kg
Height (h) = 50 cm = 0.5 m
Gravitational acceleration (g) ≈ 9.8 m/s²
Putting all these values into the formula,
Potential Energy = 20 kg × 9.8 m/s² × 0.5 m
Potential Energy = 20 kg × 4.9 m²/s²
Potential Energy = 98 J
This implies that the potential energy of the ball has decreased by 98 J.
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