Question

Two objects undergo an elastic collision. Object 1 has a mass of 1.35 kg and object 2 a mass of 3 kg. Just prior to the collision, object 1 has a kinetic energy of 77 J and object 2 is at rest. What is the initial velocity of Object 1? What is the total kinetic energy of the two cart system after the collision? What is the total momentum of the two cart system after the collision?

Answer 1

for object 1,

mass = 1.35 kg

given its initial kinetic energy = KE _initial = 77 J = 0.5 m * v ²

=> 77 = 0.5 * 1.35 * v²

=> v= 10.68 m/s

An elastic collision is one in which the total kinetic energy of the two colliding objects is the same before and after the collision. Thus, for an elastic collision we can write

since initially object two is at rest, its velocity is 0 and hence kinetic energy is 0

now the initial total kinetic energy will be 77 + 0 J = 77 J

now, the final total kinetic energy will be 77 J

c)

We are clearly considering a system in which there is zero net external force . Hence, the total momentum of the system is a conserved quantity. Equating the total momenta before and after the collision, we obtain

so, the total monetum remains conserved.

we can find the final total momentum, by calculating the initial total momentum of the system .

initial momentum = 1.35kg * 10.68 m/s + 3kg * 0 m/s

= 14.418 kgm/ s = final momentum