What does perfectly elastic mean in physics

First, the equation for conservation of momentum for two objects in a one-dimensional collision is. The equation assumes that the mass of each object does not change during the collision. This video covers an elastic collision problem in which we find the recoil velocity of an ice skater who throws a ball straight forward. To clarify, Sal is using the equation. Now, let us turn to the second type of collision. An inelastic collision is one in which objects stick together after impact, and kinetic energy is not conserved.

This lack of conservation means that the forces between colliding objects may convert kinetic energy to other forms of energy, such as potential energy or thermal energy. The concepts of energy are discussed more thoroughly elsewhere. For inelastic collisions, kinetic energy may be lost in the form of heat. Two objects that have equal masses head toward each other at equal speeds and then stick together. The two objects come to rest after sticking together, conserving momentum but not kinetic energy after they collide.

Some of the energy of motion gets converted to thermal energy, or heat. Since the two objects stick together after colliding, they move together at the same speed. This lets us simplify the conservation of momentum equation from. Ask students what they understand by the words elastic and inelastic. Ask students to give examples of elastic and inelastic collisions. This video reviews the definitions of momentum and impulse. It also covers an example of using conservation of momentum to solve a problem involving an inelastic collision between a car with constant velocity and a stationary truck.

How would the final velocity of the car-plus-truck system change if the truck had some initial velocity moving in the same direction as the car? What if the truck were moving in the opposite direction of the car initially? In this activity, you will observe an elastic collision by sliding an ice cube into another ice cube on a smooth surface, so that a negligible amount of energy is converted to heat.

The Khan Academy videos referenced in this section show examples of elastic and inelastic collisions in one dimension. In one-dimensional collisions, the incoming and outgoing velocities are all along the same line. But what about collisions, such as those between billiard balls, in which objects scatter to the side? These are two-dimensional collisions, and just as we did with two-dimensional forces, we will solve these problems by first choosing a coordinate system and separating the motion into its x and y components.

One complication with two-dimensional collisions is that the objects might rotate before or after their collision. For example, if two ice skaters hook arms as they pass each other, they will spin in circles. We will not consider such rotation until later, and so for now, we arrange things so that no rotation is possible.

To avoid rotation, we consider only the scattering of point masses —that is, structureless particles that cannot rotate or spin. The simplest collision is one in which one of the particles is initially at rest. The best choice for a coordinate system is one with an axis parallel to the velocity of the incoming particle, as shown in Figure 8. Because momentum is conserved, the components of momentum along the x - and y -axes, displayed as p x and p y , will also be conserved.

With the chosen coordinate system, p y is initially zero and p x is the momentum of the incoming particle. Along the x -axis, the equation for conservation of momentum is.

But because particle 2 is initially at rest, this equation becomes. Conservation of momentum along the x -axis gives the equation.

Along the y -axis, the equation for conservation of momentum is. But v 1 y is zero, because particle 1 initially moves along the x -axis. Because particle 2 is initially at rest, v 2 y is also zero. The equation for conservation of momentum along the y -axis becomes. Therefore, conservation of momentum along the y -axis gives the following equation:. Review conservation of momentum and the equations derived in the previous sections of this chapter.

Say that in the problems of this section, all objects are assumed to be point masses. Explain point masses. In this simulation, you will investigate collisions on an air hockey table. Place checkmarks next to the momentum vectors and momenta diagram options. Experiment with changing the masses of the balls and the initial speed of ball 1. How does this affect the momentum of each ball?

What about the total momentum? Next, experiment with changing the elasticity of the collision. You will notice that collisions have varying degrees of elasticity, ranging from perfectly elastic to perfectly inelastic. If you wanted to maximize the velocity of ball 2 after impact, how would you change the settings for the masses of the balls, the initial speed of ball 1, and the elasticity setting?

Hint—Placing a checkmark next to the velocity vectors and removing the momentum vectors will help you visualize the velocity of ball 2, and pressing the More Data button will let you take readings. Find the recoil velocity of a 70 kg ice hockey goalie who catches a 0. Assume that the goalie is at rest before catching the puck, and friction between the ice and the puck-goalie system is negligible see Figure 8.

Momentum is conserved because the net external force on the puck-goalie system is zero. Therefore, we can use conservation of momentum to find the final velocity of the puck and goalie system. Note that the initial velocity of the goalie is zero and that the final velocity of the puck and goalie are the same.

This simplifies the equation to. Two hard, steel carts collide head-on and then ricochet off each other in opposite directions on a frictionless surface see Figure 8. Cart 1 has a mass of 0. Cart 2 has a mass of 0.

What is the final velocity of cart 2? As before, the equation for conservation of momentum for a one-dimensional elastic collision in a two-object system is. The final velocity of cart 2 is large and positive, meaning that it is moving to the right after the collision. Suppose the following experiment is performed Figure 8. An object of mass 0. The 0. The speed of the 0. If you then shoot a bullet or arrow or other projectile into the target, so that it embeds itself into the object, the result is that the object swings up, performing the motion of a pendulum.

Since you know that the pendulum reaches a maximum height when all of its kinetic energy turns into potential energy, you can use that height to determine that kinetic energy, use the kinetic energy to determine v f , and then use that to determine v 1 i - or the speed of the projectile right before impact.

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Updated October 12, Featured Video. Cite this Article Format. Jones, Andrew Zimmerman. Perfectly Inelastic Collision. What is an Inelastic Collision in Physics?