Two gliders on an air track collide in a perfectly elastic collision. Glider A has mass 1.1 kg and is initially
travelling at a velocity of 2.7 m/s [E]. It collides head-on with glider B with mass 2.4 kg, travelling at a
velocity of 1.9 m/s [W]. Determine the final velocity of glider B using elastic collision formulas.
Momentum before = Momentum after:
M1*V1 + M2*V2 = M1*V3 + M2*V4.
1.1*2.7 + 2.4*(-1.9) = 1.1*V3 + 2.4*V4,
1.1*V3 + 2.4*V4 = -1.59.
Conservation of KE Eq:
V3 = (V1(M1-M2) + 2M2*V2)/(M1+M2).
V3 = (2.7(1.1-2.4) + 4.8*(-1.9))/(1.1+2.4) = -3.61 m/s = 3.61 m/s, west = Velocity of glider A after the collision.
To determine the final velocity of glider B after the collision, we can use the principles of conservation of momentum and kinetic energy in an elastic collision.
In an elastic collision, both momentum and kinetic energy are conserved. The formula for the conservation of momentum is:
m1v1(initial) + m2v2(initial) = m1v1(final) + m2v2(final)
Here, m1 and m2 are the masses of glider A and glider B, respectively. v1(initial) and v2(initial) are the initial velocities of the gliders, and v1(final) and v2(final) are their final velocities.
Using the given values:
m1 = 1.1 kg, m2 = 2.4 kg,
v1(initial) = 2.7 m/s [E], v2(initial) = -1.9 m/s [W], (negative because it's in the opposite direction),
Let's solve for v2(final):
m1v1(initial) + m2v2(initial) = m1v1(final) + m2v2(final)
(1.1 kg)(2.7 m/s) + (2.4 kg)(-1.9 m/s) = (1.1 kg)(v1(final)) + (2.4 kg)(v2(final))
Solving this equation will give us the final velocity of glider B, v2(final).