3.1.3 Experimental principles
According to the law of conservation of momentum,the total momentum of a system remains constant when the net external force on this system is zero or no external force exists in this system.It can be further concluded that the total momentum of a system in one direction is conserved when no external force acts in this direction or the net external force in this direction is zero.Moreover,the conservation of momentum is a very useful tool for dealing with collision processes.During the collision experiment on the air track,on the one hand,the slide friction is negligible due to the floating effect of the air track.On the other hand,the air resistance can also be ignored when the speed of the object is relatively small.As a result,the collision system along the horizontal direction on the air track can be approximately regarded as a system with no external force so the total momentum before the collision is the same as that afterwards.
Assuming that the masses of the two sliding blocks are m1 and m2 respectively,and their velocities before the collision are v10 and v20,and the velocities after the collision are v1 and v2.According to the law of conservation of momentum:
1)Elastic recovery coefficient
The elastic recovery coefficient e is the ratio of the absolute value of relative velocity of two bodies after the collision to that before the collision,which can be expressed as:
2)Classification of collision motions
According to the elastic recovery coefficient,collision motion can be divided into the following three categories:
(1)When e is equal to 1,it is a completely elastic collision.In this case,the collision object is made up of elastic material,and the deformation after collision can be completely recovered,so the momentum and mechanical energy of such collisions are conserved.
(2)When 0＜e＜1,it is an incompletely elastic collision.In this case,the collision object has certain plasticity and the deformation after collision cannot be completely recovered.Moreover,the lost kinetic energy can be transformed into other types of energy,such as thermal or potential energy.Therefore,the total momentum of such collisions is conserved,but the mechanical energy is not.
(3)When e is equal to 0,it is called a completely inelastic collision.In this case,the two objects stick together and move at the same speed as the result of the collision,so the momentum of such collision is conserved,but there will be more lost mechanical energy of the object.
3)Verification of the law of conservation of momentum by the incomplete elastic collision
During the experiment,two sliding blocks with the mass of m1 and m2(m1＞m2)are used and the sliding block 2(the smaller one)is put between the two photoelectric gates,where v20=0,and then we push the sliding block 1(the bigger one)with the velocity v10 to collide the sliding block 2.After the collision,the velocities of the two sliding blocks become v1 and v2 respectively.According to the law of conservation of momentum:
The kinetic energy changes before and after collision can be expressed as:
According to Equation(3.1.3)and Equation(3.1.4),as long as the masses of the two sliding blocks,the velocities v10,v1,v2 of the sliding blocks before and after the collision are measured,the conservation of momentum can be verified and then the change of kinetic energy before and after the incomplete elastic collision can be calculated.(https://www.daowen.com)
During the actual moving process,the sliding blocks will move at a certain acceleration over the“leveling”air track.The reason can be interpreted in the following:on the one hand,the air resistance can introduce the damping effect at a certain extent.One the other hand,it is very difficult to absolutely level the track.Also,a little bend on the track can exist.Therefore,the difference between the speed measured by the photoelectric door and the actual movement speed is inevitable and the corresponding speed correction must be conducted.
According to Figure 3.1.2,the three accelerations can be measured and the corresponding velocity can be corrected.In Figure 3.1.2,two sliding blocks are placed at the collision positions C and D,which are respectively corresponding to the center position of the light block of the two sliding blocks.A and B are in the actual measurement position for the sliding block speed during the experiment.
Figure 3.1.2 Schematic diagram of velocity correction
(1)Assuming that the distance between A and C is s10,and the velocity of the big sliding block 1 passing through door A is measured as v1A,and then move door B to position C while keeping door A motionless,the acceleration of the sliding block 1 between A and C is measured as a10.It can be expressed as:
(2)Assuming that the distance between B and C is s1,and the velocity of the big sliding block 1 passing through door B is measured as v1B,and then move door B back to position B,and move door A to position C,and the acceleration of sliding block 1 between C and B is measured as a1.It can be expressed as:
(3)Assuming that the distance between D and B is s2,and the velocity of the small sliding block 2 passing through door B is measured as v2B,and then move door A to position D while keeping door B motionless,and the acceleration of sliding block 2 between D and B is measured as a2.It can be expressed as:
4)Verification of the law of conservation of momentum by the complete inelastic collision
When a completely inelastic collision occurs between two objects,the elastic recovery coefficient e=0.We place the sliding block 2 between the photoelectric gate A and B,and v20=0,and then the sliding block 1 collides with the sliding block 2 with the velocity v10.After the collision,the two sliding blocks stick together and move at the same velocity v2.According to the momentum conservation formula,it can be expressed as:
The energy loss during the collision is
The corrections of velocity v10 and v2 are similar to that in Figure 3.1.2.
