For simplicity, assume the meteor is traveling vertically downward prior to impact. This enables us to solve for the maximum force.ĭefine upward to be the + y-direction. Next, we choose a reasonable force function for the impact event, calculate the average value of that function Equation 9.4, and set the resulting expression equal to the calculated average force. We then use the relationship between force and impulse Equation 9.5 to estimate the average force during impact. Using the given data about the meteor, and making reasonable guesses about the shape of the meteor and impact time, we first calculate the impulse using Equation 9.6. Therefore, we’ll calculate the force on the meteor and then use Newton’s third law to argue that the force from the meteor on Earth was equal in magnitude and opposite in direction. ![]() It is conceptually easier to reverse the question and calculate the force that Earth applied on the meteor in order to stop it. (credit: modification of work by “Shane.torgerson”/Wikimedia Commons) The amount by which the object’s motion changes is therefore proportional to the magnitude of the force, and also to the time interval over which the force is applied.įigure 9.7 The Arizona Meteor Crater in Flagstaff, Arizona (often referred to as the Barringer Crater after the person who first suggested its origin and whose family owns the land). Alternatively, the more time you spend applying this force, again the larger the change of momentum will be, as depicted in Figure 9.5. Clearly, the larger the force, the larger the object’s change of momentum will be. Suppose you apply a force on a free object for some amount of time. ![]() ![]() The purpose of this section is to explore and describe that connection. This indicates a connection between momentum and force. Therefore, if an object’s velocity should change (due to the application of a force on the object), then necessarily, its momentum changes as well. We have defined momentum to be the product of mass and velocity. Apply the impulse-momentum theorem to solve problems.This means that the velocity of the center of mass will change accordingly.By the end of this section, you will be able to: In the context of collisions, the total momentum before and after the collision must be the same, assuming no external forces are acting on the system.For a closed system, if no external forces are acting on it, the total momentum of the system will remain constant, which means that the velocity of the center of mass will also remain constant.In other words, if the total momentum of a system of objects increases, the velocity of the center of mass will also increase, and if the total mass of a system of objects increases, the velocity of the center of mass will decrease.The center of mass of a system of objects will have a velocity that is directly proportional to the total momentum of the system and inversely proportional to the total mass of the system.The total momentum of a system of objects is equal to the sum of the momenta of all the individual objects in the system.The momentum of an object is equal to its mass multiplied by its velocity, represented mathematically as p = m*v.Here are some key things to remember when solving a problem asking for the velocity of the center of mass: In a collision, the total impulse experienced by the two colliding objects must be equal and opposite, this is also known as Newton's third law.The conservation of momentum states that the total momentum of a closed system remains constant, unless acted upon by an external force.The impulse-momentum theorem states that the impulse applied to an object is equal to the change in momentum of the object, mathematically represented as J = Δp.Impulse can be used to analyze the motion of an object in a resistive medium, such as air resistance or friction. ![]() Impulse can be used in the context of both elastic and inelastic collisions, where inelastic collisions are defined as collisions where kinetic energy is not conserved and elastic collisions are defined as collisions where kinetic energy is conserved.Impulse can also be used to find the force required to stop an object or change its velocity by a certain amount in a specific period of time.Impulse can be used to find the final velocity of an object after a force has been applied for a given period of time.Impulse can be used to analyze the effect of forces on moving objects, such as during collisions.Impulse has the same effect on an object as a constant force applied over a certain period of time.Impulse is the product of force and time, represented mathematically as J = F*Δt.
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