A smallish SUV of mass 750kg runs into the back of my subcompact 400kg car at 2

Question

A smallish SUV of mass 750kg runs into the back of my subcompact 400kg car at 2 m/s while I am stopped at an intersection. He smooshes my bumper and attaches to me: 2 seconds later we come to a stop. (a)Is this an elastic or inelastic collision? Is it reversible or irreversible? Is it a conservative or non-conservative? (b)Let's assume no external forces act on the system of the two automobiles during the collision, which is usually a pretty good assumption. Find the final velocity of the combined lump of cars immediately after the collision. (c) Just to review, what is the average acceleration of the lump of automobiles from immediately after the collision to when it stops 2 seconds later? How far does the lump travel before it stops? (d) What is the energy dissipated from the collision in the two-car system? Where did all that energy go(that is, what is the physically observable evidence of what that extra energy went into doing)?

Explanation / Answer

From the given question,

mass of SUV(m1)=750 kg

initial velocity of SUV(u1)= 2m/s

mass of car(m2)=400 kg

initial velocity of car(u2)=0 m/s

Time taken to stop(t)=2sec

a) It is an inelastic collision. It is irreversible and non-conservative interaction.

b) using conservation of momentum,

m1u1 + m2u2= (m1+m2)v

(750 x 2) + (400 x 0)=(750+400)v

v=1500/1150=1.3 m/s

final velocity of combined lumps of car immediately after collision is 1.3 m/s

c)u=1.3, v1=0, t=2

v1=u+at

0=1.3+a(2)

a= -0.65 m/s2

v12=u2+2as

0=1.32-2(0.65)(s)

s=1.3 m

average acceleration of lump of automobiles immediately after collision is -0.65m/s2

The lump travel 1.3m before it stops.

d)E1= (1/2)(750)(22)+0=1500J

E2=(1/2)(750+400)(1.32)=971.75J

Energy lost=1500-971.75=528.25J

The energy is lost as heat.

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