![]() ![]() The law of conservation of momentum can be mathematically expressed in several different ways. The concept of kinetic energy will be discussed further in Module 5 of this course. An example of an inelastic collision is the head-on collision of two automobiles where part of the initial kinetic energy is lost as the metal crumples during the impact. In an inelastic collision, momentum is conserved, but system kinetic energy is not conserved. ![]() A common example of an elastic collision is the head-on collision of two billiard balls of equal mass. In an elastic collision, both momentum and kinetic energy (i.e., energy due to an objects velocity) are conserved. The development of the law of conservation of momentum does not consider whether the collision is elastic or inelastic. That is, the momentum of the bullet ( m Bv B) is equal to the momentum of the gun ( m Gv G), but of opposite direction. When the gun is fired, the momentum of the recoiling gun is equal and opposite to the momentum of the bullet. If the object is at an altitude of 30 km (18.63 mi), then the value of ( g) is as follows: If the object is a significant distance from the earth, we can demonstrate that ( g) is not a constant value but varies with the distance (altitude) from the earth. The mass ( m 1) of the object cancels, and the value of ( g) can be determined as follows since a = g by substituting ( g) for ( a) in the previous equation. Setting these two equations equal to each other yields the following. Second, we must understand that the force of attraction ( F) in Equation 3-2 for the object is equal to the object's weight ( F) as described in Equation 3.1. We already know this value to be 9.8 m/sec 2 (or 32.17 ft/sec 2), but it can be calculated using Equation 3-2.įirst, we will assume that the earth is much larger than the object and that the object resides on the surface of the earth therefore, the value of r will be equal to the radius of the earth. Using this universal law of gravitation, we can determine the value of g (gravitational acceleration constant), at the surface of the earth. Universal constant of gravitation (6.673×10 -11 m 3/kg-sec 2 or 3.44×10 -8 lbm*ft 2/slug 2)ĭistance between the centers of the two objects (m or ft) Newton expressed the universal law of gravitation using Equation 3-2.įorce of attraction (Newton = 1 kg-m/sec 2 or lbf) For any two masses, the force is directly proportional to the product of the two masses and is inversely proportional to the square of the distance between them." "Each and every mass in the universe exerts a mutual, attractive gravitational force on every other mass in the universe. It is known as the universal law of gravitation and is stated as follows. One additional law attributed to Newton concerns mutual attractive forces between two bodies. This principle holds for all forces, variable or constant, regardless of their source. Thus, the downward force exerted on a desk by a pencil is accompanied by an upward force of equal magnitude exerted on the pencil by the desk. It states that forces always occur in pairs of equal and opposite forces. The third law is basic to the understanding of force. Newton's third law of motion states "if a body exerts a force on a second body, the second body exerts an equal and opposite force on the first." This law has also been stated as, "for every action there is an equal and opposite reaction." Thus, equation 3-1 becomes F = mg for this case. When dealing with this type of problem, we designate the acceleration, g, which equals 9.8 m/sec 2 or 32.17 ft/sec 2 ( g is called gravitational acceleration constant). In this special case, F is the force, or weight, caused by the gravitational acceleration of the earth acting on the mass, m, of the object. Equation 3-1 can be used to calculate an objects weight at the surface of the earth. Also, Newton's first law is actually a consequence of this second law, since there is no acceleration when the force is zero, and the object is either at rest or moving with a constant velocity. This law is used to define force units and is one of the most important laws in physics. ![]()
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