Two dogs are playing on an icy pond (you know eventually they are going to run i

Question

Two dogs are playing on an icy pond (you know eventually they are going to run into each other, right?). To the right is an x vs. t graph of the collision between the two dogs. Dog 1 has an inertia of 1 kg (very similar to a standard cart). Dog 2 has an unknown inertia. What are the initial and final velocities of both dogs? What are the changes in the velocities of both dogs? Find the inertia of dog 2. Is the collision between the dogs explosive, elastic, inelastic, or totally inelastic? Explain how you determined your answer. If the collision is elastic, describe the motion of the two dogs. If the collision is inelastic, determine how much energy is dissipated in the collision. If it is explosive, where might the energy have come from?

Explanation / Answer

(a)As seen the slope of x vs t graph will gives us the velocity

for dog 1

initial velocity=(4-5)/1=-1 m/s

for dog 2

initial velocity =(3+3)/(1)=6 m/s

(b)

for dog 1

final velocity=5.4-5/1=0.4 m/s

for dog 2

final velocity=-1-3/1=-4 m/s

(c)conserving momentum

1*(-1)+m*6=1*0.4-m*4

we got m=inertia of dog 2=1.4/10=0.14 kg

(d)

initial kinetic energy=0.5*1*1 +0.5*0.14*36=3.02 J

final energy=1.2 J

As final energy is less so collision is inelastic

energy dissipated=1.82 J

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