Answer to Question #289984 in Physics for Sally

Question #289984

In a road accident, a van of mass 1500 kg moving at a speed of 28m * s ^ - 1 ran into the back of a car of mass 900 kg moving in the same direction at a speed of 11m * s ^ - 1 . As a result of the impact, the car was pushed forward at a speed of 18m * s ^ - 1 .




a Calculate the velocity of the van immediately after the impact.




b Calculate:




i the loss of kinetic energy of the van, ii the gain of kinetic energy of the car,




iii the total change of kinetic energy of the two vehicles.

1
Expert's answer
2022-01-23T16:13:38-0500

a. By conservation of momentum:


mv+MV=mu+MU, U=mv+MVmuM=23.4 m/s.mv+MV=mu+MU,\\\space\\ U=\dfrac{mv+MV-mu}{M}=23.4\text{ m/s}.


b i. The loss of kinetic energy of the van:


ΔKEv=12M(U2V2)=177330 J.\Delta KE_v=\dfrac12M(U^2-V^2)=177330\text{ J}.

b. ii. The gain of kinetic energy of the car:


ΔKEc=12m(u2u2)=91350 J.\Delta KE_c=\dfrac12m(u^2-u^2)=91350\text{ J}.

b. iii. The total change of kinetic energy of the two vehicles:


ΔKEc=ΔKEv+ΔKEc=268680 J.\Delta KE_c=\Delta KE_v+\Delta KE_c=-268680\text{ J}.



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