CONSERVATION OF MOMENTUM AND ENERGY IN COLLISIONS

 

GOAL

            The goal of this work is to investigate the relationship between total momentum (and energy) of two carts before and after elastic and inelastic collisions.

 

PREREQUISITES

                                 R.D. Knight, Physics, Chapters 9, 10.

 

EQUIPMENT

                         Pasco device

                         Two motion censors

                         Air track with blower

                         Two air track carts

                         Scale

 

THEORY

                 The momentum of an object is the product of its mass and its velocity. According to the law of Conservation of Momentum, the total initial momentum of the system (the sum of momenta of all objects prior to a collision) equals to the total final momentum of the system (the sum of momenta of all objects after the collision) if there are no external forces acting on the system. Total momentum is conserved during both elastic and inelastic collisions. The law is illustrated on the picture below for the binary collision.

 

 

At the same time, the mechanical energy (kinetic energy plus potential energy) is conserved only in the perfectly elastic collisions. During the inelastic collision we have deal with transformation of mechanical energy into the heat.

 

PROCEDURE

1.      Setup the carts for elastic collision attaching the rubber to one of the

      cart.

2.      Use the scale to measure the mass of each cart and record the values.

3.       Start your Pasco device and push F4 button. Highline the option “Two graphs” and click √ button. You have to see two x- and y- axis on the screen.

4.      Figure out which graph (upper or lower) corresponds to left (right) sensor. To do that block one of the sensor and gently initiate collision of carts. The blocked sensor will produce horizontal line on the screen. NOTE, that sensors and reflection screens on carts have to be appropriately mounted. In case of the absence of signal on the screen check sensors and reflection screens – you probably have to change the position of the sensor or to rotate the reflection screen.

5.      Practice a few times to record collision event. Stop Pasco device a few seconds after collision and rescale you picture. Use F1 button for this purpose. Remember, you can delete your trials using the buttons √ > √ and picking up relevant item from menu. In ideal case you have to see perfect triangle on the screen. The slopes of the triangle sides determine yours initial and final velocities of the cart. NOTE, that the appropriate sign has to be ascribed to the velocities during calculation of the initial and final momenta.

6.      Repeat elastic collision three times. Every time record data (carts’ velocities) in the Table 1.

7.      Setup the carts for inelastic collision attaching the cork to one of the

cart.

1.      Repeat items 2-7 for inelastic collision recording your data in Table 2.

 

Table 1. Elastic Collision.

                                    Mass of the left cart: ___________________________________

                                    Mass of the right cart: __________________________________

 

N of trial

V1i (m/s)

V1f (m/s)

V2i (m/s)

V2f (m/s)

Pi (kg·m/s)

Pf (kg·m/s)

Ei

(J)

Ef

(J)

|Pi-Pf|

|Ei-Ef|

1

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

Table 2. Inelastic Collison.

                                    Mass of the left cart: ___________________________________

                                    Mass of the right cart: __________________________________

 

N of trial

V1i (m/s)

V1f (m/s)

V2i (m/s)

V2f (m/s)

Pi (kg·m/s)

Pf (kg·m/s)

Ei

(J)

Ef

(J)

|Pi-Pf|

|Ei-Ef|

1

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

ANALYSIS

1.      Make all necessary calculation to fill both Tables completely.

2.      Explain your results (mainly content of two last columns in each Table).