1. Particle 1 has 1/2 the mass of Particle 2, yet they both have the same kineti

Question

1. Particle 1 has 1/2 the mass of Particle 2, yet they both have the same kinetic energy. Compare the momenta of two particles.

2. Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?

Explanation / Answer

1. Given: m1= (1/2) m2.

KE1= KE2

Solution :

Both particles have the same kinetic energy ,

KE1= KE2

(1/2) m1v12= (1/2) m2v22

(1/2)m2v12= m2v22

v1= 2 v2

Now using momentum equation .

For particle 1: P1= m1v1= (1/2)m2(2)v2

For particle 2: P2= m2v2

P1/P2= (1/2)m2v2/m2v2

i.e. P1= P2/2

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