Collision in One Dimension—Classroom Set
Introduction
Discover some of the basic laws of physics by studying simple onedimensional collisions. Smash one ball into a series of three or four balls and observe what happens. Predict how colliding two ball bearings at the same time will affect the collision results?
Concepts
 Collisions
 Conservation of energy
 Conservation of momentum
Background
When an object is set in motion, the object has a property known as momentum. Momentum is calculated by multiplying the mass of the object by its velocity. A fundamental principle of physics is that the momentum of a system of objects always remains constant. This principle is known as the conservation of momentum. If objects within a system collide, the momentum of the individual objects before and after a collision may change, but the total momentum of the system will remain constant.
There are two types of collisions—elastic and inelastic. An elastic collision occurs when the objects that collide separate after the collision. An example of an elastic collision is the collision between a baseball and a bat. An inelastic collision occurs when the objects that collide stick together and move as one object after the collision. An example of an inelastic collision is when the baseball hits the catcher’s mitt and stops. In every collision, elastic or inelastic, momentum is always conserved. The main difference between the two types of collisions is that for an elastic collision, the kinetic energy of the system also remains the same. The conservation of energy principle does not apply to an inelastic collision because in an inelastic collision much of the energy is lost as heat and sound due to frictional forces that arise when the objects deform and “stick” together.
In this activity, elastic collisions occur because the ball bearings separate and one set continues to move after the collision. Since these are elastic collisions, both the conservation of momentum and the conservation of kinetic energy principles apply. The conservation of energy principle limits the number of ball bearings that can be knocked away from the stationary series. No matter how fast a single colliding ball bearing hits the stationary series of ball bearings only one ball bearing will be knocked away(provided they are the same mass). If two ball bearings collide with the stationary ball bearings, two ball bearings will be knocked away.
Example A moving ball with mass (M) and velocity (V) collides into a stationary series of three ball bearings, each with the same mass as the colliding ball. The momentum and kinetic energy of the colliding ball is MV and ½MV^{2}, respectively. The colliding ball comes to a complete stop after the collision and its momentum and kinetic energy are transferred to the ball bearing at the end of the series. Momentum is conserved during every collision so the ball bearing is knocked away with velocity V (momentum equal to MV). The kinetic energy of the ball bearing is equal to ½MV^{2}, clearly showing that energy has also been conserved.
Assume instead that two ball bearings were knocked away by the one colliding ball bearing. In order to conserve momentum, the two ball bearings (2M) would be knocked away from the series with half the velocity of the colliding ball [MV = 2M(½)V].However, the kinetic energy of this twoball system would then be equal to ½(2M)(V/2)^{2}, or ¼MV^{2}. The kinetic energy of the twoball system is onefourth the original kinetic energy and is clearly not conserved as it should be during an elastic collision. Therefore, this result is not possible. One colliding ball will knock away only one ball (provided the masses are equal). One ball cannot knock away two or more balls no matter how fast it is traveling.
Materials
Metal Vtrack Rubberbands, 2 Steel ball bearings, ¾" diameter, equal mass, 5 Wooden feet, 2
Safety Precautions
The materials used in this activity are nonhazardous. Please follow all normal laboratory safety precautions.
Procedure
 Place three steel ball bearings in the middle of the Vtrack. The three ball bearings must be in contact with each other (see Figure 1).
 Roll one ball bearing into the threeball bearing system from the left. Record the results of the collision in the data table. (Did the colliding ball stop or recoil? How many ball bearings were knocked away from the stationary ballbearing series? How did the speed of the knockedaway ball compare to the initial speed of the colliding ball?)
{11874_Procedure_Figure_1}
 Repeat steps 1 and 2. For step 2, however, roll the colliding ball with more speed at the stationary ball bearings. Record the results of the collision in the data table.
 Repeat step 1.
 Roll a system of two, nearly touching ball bearings into the threeball system. To ensure that the ball bearings stay in contact as they roll, push on the ball bearing of the twoball series that is farthest away from the series of stationary ball bearings. This way both ball bearings will roll with the same speed and remain close together. Also, release the ball bearings a short distance away from the stationary ball bearings. Record the results of the collision in the data table.
 Repeat steps 4 and 5. For step 5, increase the speed of the two colliding ball bearings. Make sure the two rolling ball bearings are nearly touching as they make contact with the stationary ball bearings. Record the results of the collision in the data table.
 Place four steel ball bearings in the middle of the angle track. The four ball bearings must be in contact with each other.
 Repeat steps 2 and 3. Record the results of the collisions in the data table.
 Answer the PostLab Questions.
 Consult your instructor for appropriate storage procedures.
