(lloyd) Law Of Conservation Of Linear Momentum.pptx
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Law of Conservation of Linear Momentum Law of Conservation of Linear Momentum
Law of Conservation of Linear Momentum β’
The acceleration in the equation of Newtonβs second law may be written in terms of change in velocity per unit time. In symbols,
β’
Multiplying both sides by t gives
π=
π(π£βπ£0 ) π‘
ππ‘ = ππ£ β π£0 β’
The product of force and time during which the force acts is called impulse. Linear momentum, at simply momentum, is the product of the mass of a moving object and its velocity. The above equations represents the impulse-momentum theorem and is considered to be an alternative statement of Newtonβs second law of motion. Using p as a symbol for momentum,
π = ππ£
Law of Conservation of Linear Momentum β’
Possessed by all moving objects, momentum is a vector quantity, with a direction the same as that of the velocity. Its SI unit is kg m/s,
β’
Momentum is the best explained by considering an isolated closed system. As an additional characteristics, an isolated system does not have any external forces acting on it. A closed system is one where there is no increase or decrease in the mass of the system. A single system may be both closed and isolated. For an isolated closed system with two interacting bodies, the total momentum before interaction is equal to the total momentum after interaction. This principle is called conservation of momentum, which applies to linear momentum and angular momentum. The succeeding discussion will focus on linear momentum. For two interacting bodies of masses π1 and π2 π1 π£1 + π1 π£1π + π2 π£2π
Law of Conservation of Linear Momentum β’
Where subscripts I and f mean initials and final states, respectively. Note that momentum is a vector quantity, thus its direction must always be taken into consideration in the equations. Objects moving to the right have positive momentum; those moving to the left have negative momentum.
β’
A 5,000 kg truck moving at 15 m/s collides with a 2,000 kg stationary car. The two vehicles stick together and move as one after collision. (a) Find their common velocity after colliding. (b) Determine whether the collision is elastic or inelastic.
Given: π1 = 5 000 kg
π£1 = 15 m/s
π2 = 2 000 kg
π£2 = 0 m/s
Law of Conservation of Linear Momentum Solution: β’
a. In the equation for the law of conservation of momentum, π£1π and π£2π may be represented by v, and the two masses may be combined because they moved as one after collision. Note that π£2π = 0
π1 π£1π + π2 π£2π = π1 π£1π + π£2π π1 π£1π + π2 π£2π = (π1 + π2 ) π£ π£=
π1 π£1π π1
+
π2 π£2π π2
=(5000 kg) (15 m/s) +0 5 000 kg + 2 000 kg = 10.7 m/s
Law of Conservation of Linear Momentum b. To determine whether collision is elastic or not, check whether kinetic energy is conserved or not.
β’
πΎπΈππππ‘πππ =
1 2
2 π1 π£1π =
1 2
πΎπΈππππ‘πππ =
1 2
(π1 +π2 )π£ 2 =
(5000 kg) (15 m/s) ^2 = 562500 J 1 2
(5000 kg + 2000 kg) (10.7 m/s) ^2 = 400715 J
Since kinetic energy is not conserved, the collision is inelastic.
Law of Conservation of Linear Momentum β’
Conservation Laws
In everyday usage, the word conservation denotes wise use of something like energy. In physics, the term refers to a situation where the amount of a physical quantity remains constant. It is a βbefore-and-after interactionβ look at a system. Conservation laws are formulated in physics to offer a different approach to mechanics. β’
Law of Conservation of Energy
The law of conservation of energy states that energy can neither be created nor destroyed, but can be changed from one form to another. A car engine burns fuel, converting the fuelβs chemical energy into mechanical energy to make the car move. Windmills transform the windβs energy into mechanical energy in order to turn turbines, which then produce electricity. Solar cells convert radiant energy from the sun to electrical energy, which in turn may be converted to light, sound, or heat energy in homes.
Law of Conservation of Linear Momentum β’
Law of Conservation of Mass
The law of conservation of mass dates from Antoine Lavoisierβs 1789 discovery that in chemical reactions, the total mass of the reactants equals the total mass of the products. The total mass of an isolated system is constant. An isolated system as referred to here is system where no mass enters or leaves during an interaction. With his famous equation E=mc^2, Albert Einstein showed that mass and energy are equivalent. The equation shows that mass can be converted to energy and vice versa. The mass-energy equivalence accounts for the unaccounted mass, particularly in nuclear reactions. As a results of this, this two conservation laws were merge into one the law of conservation of mass and energy.
Law of Conservation of Linear Momentum β’
Conservation of momentum is experienced in some familiar situations. When a person walks on his skateboard in one direction, the skateboard moves in the opposite direction. The same situation may be observed when he steps from a small boat onto a dock. As a person steps towards the dock, the boat moves away from the dock, and he may fall into the water. Similarly, when a gun is fired, the bullets moves forward, but the gun recoils in the opposite direction. In these situations, the momentum before interaction is zero. When one of the interacting bodies moves forward, it acquires momentum in the forward direction. Consequently, the other body must move backward to keep the total momentum zero.
β’
One of the most important applications of the law conservation of linear momentum is in the analysis of collisions, which may be elastic or inelastic. In an elastic collision, the total kinetic energy of the system is conserved, which means that the sum of the kinetic energies of the interacting bodies before and after collision are equal. In an inelastic collision, some kinetic energy is changed into other forms of energy. Recall that the kinetic energy (KE) of a body is given by the formula. KE =
β’
1 2
mv^2
Where m is the mass and v is the speed of the body. The SI unit for kinetic energy is kg m^2/ s^2 or joule (J.)
Law of Conservation of Linear Momentum β’
The acceleration in the equation of Newtonβs second law may be written in terms of change in velocity per unit time. In symbols,
β’
Multiplying both sides by t gives
π=
π(π£βπ£0 ) π‘
ππ‘ = ππ£ β π£0 β’
The product of force and time during which the force acts is called impulse. Linear momentum, at simply momentum, is the product of the mass of a moving object and its velocity. The above equations represents the impulse-momentum theorem and is considered to be an alternative statement of Newtonβs second law of motion. Using p as a symbol for momentum,
π = ππ£
Law of Conservation of Linear Momentum β’
Possessed by all moving objects, momentum is a vector quantity, with a direction the same as that of the velocity. Its SI unit is kg m/s,
β’
Momentum is the best explained by considering an isolated closed system. As an additional characteristics, an isolated system does not have any external forces acting on it. A closed system is one where there is no increase or decrease in the mass of the system. A single system may be both closed and isolated. For an isolated closed system with two interacting bodies, the total momentum before interaction is equal to the total momentum after interaction. This principle is called conservation of momentum, which applies to linear momentum and angular momentum. The succeeding discussion will focus on linear momentum. For two interacting bodies of masses π1 and π2 π1 π£1 + π1 π£1π + π2 π£2π
Law of Conservation of Linear Momentum β’
Where subscripts I and f mean initials and final states, respectively. Note that momentum is a vector quantity, thus its direction must always be taken into consideration in the equations. Objects moving to the right have positive momentum; those moving to the left have negative momentum.
β’
A 5,000 kg truck moving at 15 m/s collides with a 2,000 kg stationary car. The two vehicles stick together and move as one after collision. (a) Find their common velocity after colliding. (b) Determine whether the collision is elastic or inelastic.
Given: π1 = 5 000 kg
π£1 = 15 m/s
π2 = 2 000 kg
π£2 = 0 m/s
Law of Conservation of Linear Momentum Solution: β’
a. In the equation for the law of conservation of momentum, π£1π and π£2π may be represented by v, and the two masses may be combined because they moved as one after collision. Note that π£2π = 0
π1 π£1π + π2 π£2π = π1 π£1π + π£2π π1 π£1π + π2 π£2π = (π1 + π2 ) π£ π£=
π1 π£1π π1
+
π2 π£2π π2
=(5000 kg) (15 m/s) +0 5 000 kg + 2 000 kg = 10.7 m/s
Law of Conservation of Linear Momentum b. To determine whether collision is elastic or not, check whether kinetic energy is conserved or not.
β’
πΎπΈππππ‘πππ =
1 2
2 π1 π£1π =
1 2
πΎπΈππππ‘πππ =
1 2
(π1 +π2 )π£ 2 =
(5000 kg) (15 m/s) ^2 = 562500 J 1 2
(5000 kg + 2000 kg) (10.7 m/s) ^2 = 400715 J
Since kinetic energy is not conserved, the collision is inelastic.
Law of Conservation of Linear Momentum β’
Conservation Laws
In everyday usage, the word conservation denotes wise use of something like energy. In physics, the term refers to a situation where the amount of a physical quantity remains constant. It is a βbefore-and-after interactionβ look at a system. Conservation laws are formulated in physics to offer a different approach to mechanics. β’
Law of Conservation of Energy
The law of conservation of energy states that energy can neither be created nor destroyed, but can be changed from one form to another. A car engine burns fuel, converting the fuelβs chemical energy into mechanical energy to make the car move. Windmills transform the windβs energy into mechanical energy in order to turn turbines, which then produce electricity. Solar cells convert radiant energy from the sun to electrical energy, which in turn may be converted to light, sound, or heat energy in homes.
Law of Conservation of Linear Momentum β’
Law of Conservation of Mass
The law of conservation of mass dates from Antoine Lavoisierβs 1789 discovery that in chemical reactions, the total mass of the reactants equals the total mass of the products. The total mass of an isolated system is constant. An isolated system as referred to here is system where no mass enters or leaves during an interaction. With his famous equation E=mc^2, Albert Einstein showed that mass and energy are equivalent. The equation shows that mass can be converted to energy and vice versa. The mass-energy equivalence accounts for the unaccounted mass, particularly in nuclear reactions. As a results of this, this two conservation laws were merge into one the law of conservation of mass and energy.
Law of Conservation of Linear Momentum β’
Conservation of momentum is experienced in some familiar situations. When a person walks on his skateboard in one direction, the skateboard moves in the opposite direction. The same situation may be observed when he steps from a small boat onto a dock. As a person steps towards the dock, the boat moves away from the dock, and he may fall into the water. Similarly, when a gun is fired, the bullets moves forward, but the gun recoils in the opposite direction. In these situations, the momentum before interaction is zero. When one of the interacting bodies moves forward, it acquires momentum in the forward direction. Consequently, the other body must move backward to keep the total momentum zero.
β’
One of the most important applications of the law conservation of linear momentum is in the analysis of collisions, which may be elastic or inelastic. In an elastic collision, the total kinetic energy of the system is conserved, which means that the sum of the kinetic energies of the interacting bodies before and after collision are equal. In an inelastic collision, some kinetic energy is changed into other forms of energy. Recall that the kinetic energy (KE) of a body is given by the formula. KE =
β’
1 2
mv^2
Where m is the mass and v is the speed of the body. The SI unit for kinetic energy is kg m^2/ s^2 or joule (J.)
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