When do inelastic collisions occur

An elastic collision occurs when the two objects "bounce" apart when they collide. Two rubber balls are a good example. In an elastic collision, both momentum and kinetic energy are conserved. Almost no energy is lost to sound, heat, or deformation. The first rubber ball deforms, but then quickly bounces back to its former shape, and transfers almost all the kinetic energy to the second ball.

Assume friction between the ice and the puck-goalie system is negligible. See Figure. Momentum is conserved because the net external force on the puck-goalie system is zero.

We can thus 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. 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.

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. Momentum is conserved because the surface is frictionless. We chose the coordinate system so that the initial velocity is parallel to the x -axis, and conservation of momentum along the x - and y -axes applies. The losses can be "taken into account", at least theoretically, in formulae associated with increased internal energy which lumps the effect of increased molecular motion and friction due to permanent deformation , heat transfer, and sound.

Following the collision, there will be heat transfer from the object whose temperature was elevated, to the environment, Per Newton's law of cooling. In a collision, sound energy is a very small part of the total kinetic energy loss. Moreover, sound is itself essentially kinetic energy, in this case the kinetic energy of the surrounding air that has been set into vibration motion by the vibrations of the object from the collision. Sign up to join this community.

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