Respuesta :
Answer:
initial kinetic energy = final kinetic energy = m · v²
Explanation:
Hi there!
Since the gliders collide elastically, the kinetic energy and momentum of the system after the collision are the same as before the collision.
Then, the initial kinetic energy of the system will be equal to the final kinetic energy of the system.
The equation of kinetic energy for each glider is the following:
KE = 1/2 · m · v²
Where:
KE = kinetic energy.
m = mass of the glider.
v =velocity of the glider.
The sum of the kinetic energies of each glider is the kinetic energy of the system. Then, the initial kinetic energy of the system will be:
initial KE = 1/2 · m · v² + 1/2 · m · v²
initial KE = m · v²
Since the initial kinetic energy of the system is equal to the final kinetic energy of the system:
final KE = m · v²
Using the equation of momentum of the system:
initial momentum = m · v + m · (-v) = m (v-v) = 0
The initial and final momentum of the system is zero because both vectors cancel each other for being of the same magnitude but of opposite direction.
The initial kinetic energy and what is the final kinetic energy, in terms of m and v
Initial kinetic energy = mv²
Initial kinetic energy = mv²Final kinetic energy = mv²
We are told that the two gliders have equal mass and equal and opposite initial velocity
Thus;
m1 = m2 = m
Initial velocity of first glider u1 = v
Initial velocity of second glider; u2 = -v
Now, the momentum and energy equation talked about is;
m1•u1 + m2•u2 = m1•v1 + m2•v2 (for momentum)
½m1•(u1)² + ½m2•(u2)² = ½m1•(v1)² + ½m2•(v2)² (energy)
The left hand side of the second equation gives the total initial kinetic energy before collision while the right hand side gives the total final kinetic energy after collision.
Thus, plugging in the relevant values into the left hand side of the energy equation gives;
½mv² + ½m(-v)²
>> ½mv² + ½mv²
>> Inertia kinetic energy = mv²
From conservation of energy, total initial kinetic energy must be equal to total final kinetic energy.
Thus;
Final kinetic energy = mv²
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