Physics 2211, Lab 12: Kinetic Energy in Collisions

Eric Murray, Spring 2006

Required Advance Reading

In a collision, a large force acts between two objects for a short time. Other forces acting on the objects may be considered negligible for that short time, so the momentum, P, of the system of objects is conserved. For two objects in one dimension

P_i = P_f  ⇒  m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f

where 1 and 2 represent the two objects, and i and f represent initial and final states (i.e., before and after the collision).

If the collision is elastic then the total kinetic energy, K, of the system is the same before and after the collision. (During the collision, kinetic energy may temporarily be stored as potential energy.) In other words, the change in kinetic energy, ΔK, is zero.

On the other hand, if the collision is inelastic then the kinetic energy of the system will not be the same before and after the collision. If a collision between two objects is perfectly inelastic then the two objects stick together (v_1f = v_2f) and there is a maximum kinetic energy loss. (In general, all the kinetic energy isn't lost, since that would require v_1f = v_2f = 0, which would be inconsistent with momentum being conserved.) Before coming to lab, you should find a general expression for the fractional kinetic energy loss, ΔK/K_i, for the special case v_2i = 0 which will be examined in these experiments.

There is an additional experimental complication, as your first experiment will demonstrate. At the speeds your object m₁ is likely to be travelling, friction will have a significant effect. That is, kinetic energy would be lost even if there were no collision! This can be compensated for by using as v_1i, not the actual speed of the object before the collision, but the speed the object would have had at the time after the collision, had the collision not taken place. Fortunately, the frictional force is roughly constant, so the acceleration due to friction is roughly constant, and the velocity of the object m₁ decreases linearly with time. By fitting a line to the velocity data for m₁ before the collision, the equation of the line (slope and intercept) can be used to calculate this predicted v_1i. (Because the velocities of the two objects cannot be measured at exactly the same time, the after time for objects m₁ and m₂ are not quite the same. Use the average time when predicting v_1i.)

Analysis Note: Although collection of the substantial amount of data in these experiments will not take too long, analysis of the data may be quite time-consuming. Sample data and calculated results for one elastic collision are tabulated below. (Since v_2i = 0, space is saved by not listing it in the table.) Make sure you know how the analysis is performed, and can get these same results, before coming to lab. An Excel spreadsheet may be helpful in the lab, and you may want to plan it beforehand. If you spend your lab time puzzling over how to predict v_1i and calculate kinetic energies, you will probably not complete the lab on time.

Lab 12, Experiment 2. Elastic Collision.
m₁ = 977.8 g
m₂ = 475.7 g

Before				After					Results
Slope measured	Intercept measured	Predicted v1i calculated	Kinetic Energy calculated	v1f measured	Time1f measured	v2f measured	Time2f measured	Kinetic Energy calculated	ΔK calculated	ΔK/Ki calculated
-0.0430 m/s/s	0.322 m/s	0.241 m/s	28.4 mJ	0.065 m/s	1.8933 s	0.331 m/s	1.8814 s	28.1 mJ	-0.3 mJ	-1%