# Laws of Collision / demonstration track

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1 Related topics Conservation of momentum, conservation of energy, linear motion, velocity, elastic loss, elastic collision, inelastic collision. Principle The velocities of two carts, moving on a, are measured before and after collision, for both elastic and inelastic collision. Equipment 2 Tube with plug Needle with plug Fork with plug Rubber bands f.fork w/plug,10 pcs Plate with plug Magnet w.plug f.starter system Slotted weight, 10 g, black Slotted weight, 50 g, black Light barrier, compact Timer Portable Balance, OHAUS CS AC adapter included Demonstration Track, Aluminium, Length: 1.5 m Cart, low friction sapphire bearings Starter system for Weight for low friction cart, 400 g Shutter plate for low friction cart, Holder for light barrier End holder for Connecting cord, 32 A, 1000 mm, red Connecting cord, 32 A, 1000 mm, yellow Connecting cord, 32 A, 1000 mm, blue Fig. 1: P P PHYWE Systeme GmbH & Co. KG All rights reserved 1

3 Theory and evaluation In the elastic collision of two bodies having masses m1 and m2, kinetic energy and momentum are conserved: Due to the unidimensional sequence of movement, we will dispense with the vectorial notation. For a central elastic with p 2 = 0: From the contribution of the impulse p, the energies E can be calculated according to E = p 2 /2m: Fig. 2: Elastic collision: moment after the collision as functions Fig. 3: Elastic collision: energy after the collision as functions P PHYWE Systeme GmbH & Co. KG All rights reserved 3

4 Laws of Collision / Fig. 2 and Fig. 3 show the results for a sample measurement. In particular, one can see that the total impulse and the total energy before and after the collision, except for a slight loss, are equal. The comparison of the measured values with the theoretical values according to the formulas given above can be seen in Fig. 4 and Fig. 5. Fig. 4: Elastic collision: calculated momenta after the collision as functions Fig. 5: Elastic collision: calculated energies after the collision as functions In an inelastic collision, only the momentum is conserved. In addition, the velocities after the collision are equal: Therefore, The following is obtained for the energies of the two carts after the collision: 4 PHYWE Systeme GmbH & Co. KG All rights reserved P

5 The evaluation of a sample measurement (Fig. 6 and Fig. 7) shows that also for an inelastic collision, the total impulse is conserved; whereas, depending on m 1 /m 2, a substantial energy loss occurs. The theoretical curves are compared with the measured values in Fig. 8 and Fig. 9. In Fig. 9, the energy loss is additionally plotted [energy loss = E 1 (E 1 ' + E 2 ' )]. One sees that for a mass ratio of 1, the kinetic energy is reduced by exactly 50%. Fig. 6: Inelastic collision: momenta after the collision as functions Fig. 7: Inelastic collision: energy after the collision as functions Fig. 8: Inelastic collision: calculated moment after the collision as functions Fig. 9: Inelastic collision: calculated energies after the collision and energy loss as functions P PHYWE Systeme GmbH & Co. KG All rights reserved 5

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