7.4. Collisions and Conservation Principles http://www.ck12.org
7.4 Collisions and Conservation Principles
Objectives
The student will:
- Understand the difference between elastic and inelastic collisions.
- Be able to solve problems using both energy and momentum conservation.
Vocabulary
- elastic collisions:Collisons in which we assume the kinetic energy is conserved.
- inelastic collisions:Collisions where kinetic energy is not conserved.
Introduction
There is a common misconception in the study of the conservation of momentum. It is often believed that if the
kinetic energy of a system is not conserved, neither is the momentum. This is not true. Kinetic energy can be lost
in many ways. When objects collide, some of their kinetic energy invariably is transformed into heat and sound.
However, if the losses are negligible we often assume that the kinetic energy is conserved. Collisions in which
we assume the kinetic energy is conserved are calledelastic collisions. Collisions where the kinetic energy is not
conserved are calledinelastic collisions.
Elastic Collisions
We have already encountered elastic collisions, but we haven’t used the term yet. The collision between the two
marbles in a previous example was an elastic collision. The kinetic energy of the first marble was completely
transferred to the second marble.
As we have already seen, conservation principles are very useful in solving problems that would be very difficult to
solve using Newton’s Laws. It is much simpler if we need only concern ourselves with the initial and final state of a
system rather than needing a detailed mathematical description of the intervening motion.
Illustrative Example 7.4.1
A cube of mass 10.0-kg moving with a velocity of 7.00 m/s along a frictionless horizontal surface collides elastically
with a stationary ball of mass 4.00-kg as shown inFigure7.14. What are the final velocities of the cube and the
ball?
Answer:
There are two unknowns in the problem,vc fandvb f. We will therefore need a system of two equations to solve the
problem. We can readily assume that the net force acting on the system is zero and therefore the momentum of the
system is conserved. Additionally, we can further assume that the kinetic energy of the system is conserved since the
collision is elastic. Thus, we can generate two equations and two unknowns using the Conservation of Momentum