Why is inelastic collision momentum conserved

In a low speed collision, the kinetic energy is small enough that the bumper can deform and then bounce back, transferring all the energy directly back into motion. Almost no energy is converted into heat, noise, or damage to the body of the car, as it would in an inelastic collision. However, car bumpers are often made to collapse if the speed is high enough, and not use the benefits of an elastic collision.

The rational is that if you are going to collide with something at a high speed, it is better to allow the kinetic energy to crumple the bumper in an inelastic collision than let the bumper shake you around as your car bounces in an elastic collision.

Making their bumpers this way benefits the car companies: they get to sell you a new bumper, and you can't sue them for whiplash.

Elastic collisions are collisions in which both momentum and kinetic energy are conserved. The total system kinetic energy before the collision equals the total system kinetic energy after the collision. If total kinetic energy is not conserved, then the collision is referred to as an inelastic collision. The animation below portrays the elastic collision between a kg truck and a kg car. The before- and after-collision velocities and momentum are shown in the data tables.

Note that the initial velocity of the goalie is zero and that the final velocity of the puck and goalie are the same. Once the final velocity is found, the kinetic energies can be calculated before and after the collision and compared as requested.

Because the goalie is initially at rest, we know. Because the goalie catches the puck, the final velocities are equal, or. Thus, the conservation of momentum equation simplifies to. Solving for yields. Before the collision, the internal kinetic energy of the system is that of the hockey puck, because the goalie is initially at rest.

Therefore, is initially. Nearly all of the initial internal kinetic energy is lost in this perfectly inelastic collision. During some collisions, the objects do not stick together and less of the internal kinetic energy is removed—such as happens in most automobile accidents. Alternatively, stored energy may be converted into internal kinetic energy during a collision.

Figure shows a one-dimensional example in which two carts on an air track collide, releasing potential energy from a compressed spring. Figure deals with data from such a collision. Collisions are particularly important in sports and the sporting and leisure industry utilizes elastic and inelastic collisions. Let us look briefly at tennis. Recall that in a collision, it is momentum and not force that is important. So, a heavier tennis racquet will have the advantage over a lighter one.

This conclusion also holds true for other sports—a lightweight bat such as a softball bat cannot hit a hardball very far. The location of the impact of the tennis ball on the racquet is also important, as is the part of the stroke during which the impact occurs.

A smooth motion results in the maximizing of the velocity of the ball after impact and reduces sports injuries such as tennis elbow. Sports science and technologies also use physics concepts such as momentum and rotational motion and vibrations. In the collision pictured in Figure , two carts collide inelastically. Cart 1 denoted carries a spring which is initially compressed.

During the collision, the spring releases its potential energy and converts it to internal kinetic energy. The mass of cart 1 and the spring is 0. Cart 2 denoted in Figure has a mass of 0. After the collision, cart 1 is observed to recoil with a velocity of. We can use conservation of momentum to find the final velocity of cart 2, because the track is frictionless and the force of the spring is internal.

Once this velocity is determined, we can compare the internal kinetic energy before and after the collision to see how much energy was released by the spring. As before, the equation for conservation of momentum in a two-object system is. The only unknown in this equation is.

Solving for and substituting known values into the previous equation yields. The governing equation is. In other words, the sum of the external works on your system equals the change in total energy , but that doesn't tell you anything about the kinetic energy.

Energy can change forms. So if kinetic energy is lost in some collision, it went into potential, thermal, etc. The sum is not conserved because the momentum that was transferred changed differently the result of the squares. In a word, kinetic energy doesn't change linearly with speed which is obvious since it's a square. Sign up to join this community.

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