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 A using elastic collision formulas.
Conservation of Momentum:
M1*V1 + M2*V2 = M1*V3 + M2*V4.
1.1*2.7 + 2.4*(-1.9) = 1.1V3 + 2.4V4,
1.1V3 + 2.4V4 = -1.59.
Conservation of Kinetic Energy:
0.5M1*V1^2 + 0.5M2*V2^2 = 0.5M1*V3^2 + 0.5M2*V4^2.
Divide both sides by 0.5:
M1*V1^2 + M2*V2^2 = M1*V3^2 + M2*V4^2.
1.1*2.7^2 + 2.4*1.9^2 = 1.1V3^2 + 2.4V4^2,
1.1V3^2 + 2.4V4^2 = 16.7.
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 = Final velocity of Glider A.
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Two gliders collide on an air track. Glider 1 has a mass of 7.0 kg, and glider 2 has a mass of 4.0 kg. Before the collision, glider 1 had a velocity of 2.0 m/s, and glider 2 had a velocity of -5.0 m/s. If the collision is perfectly elastic, what is the total kinetic energy of both gliders after the collision?
consider the figure below. the two gliders are moving as shown in the figure and had a head on collision. if the velocity of A after impact is "-7.0" m/s. a) what is the velocity of B after collision? b) Determine the change in kinetic energy of the system.
To determine the final velocity of glider A using elastic collision formulas, you can use the conservation of momentum and energy principles.
Step 1: Calculate the initial momentum of each glider
The momentum of an object is given by the product of its mass and velocity. Calculate the initial momentum of glider A and glider B separately.
Initial momentum of glider A (pA) = mass of glider A (mA) * velocity of glider A (vA)
pA = 1.1 kg * 2.7 m/s = 2.97 kg·m/s [E]
Initial momentum of glider B (pB) = mass of glider B (mB) * velocity of glider B (vB)
pB = 2.4 kg * -1.9 m/s (since the glider B is moving in the opposite direction) = -4.56 kg·m/s [W] (negative because it's moving in the opposite direction)
Step 2: Apply the conservation of momentum
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Total momentum before collision = Total momentum after collision
pA + pB = pA' + pB'
Since glider B only collides with glider A, the momentum of glider B after the collision (pB') is zero.
pA + pB = pA' + 0
pA + pB = pA'
Step 3: Calculate the final velocity of glider A
Now, substitute the given values into the equation and solve for the final velocity of glider A (vA').
2.97 kg·m/s [E] + (-4.56 kg·m/s [W]) = mA * vA'
2.97 kg·m/s - 4.56 kg·m/s = (1.1 kg) * vA'
-1.59 kg·m/s = 1.1 kg * vA'
vA' = -1.59 kg·m/s / 1.1 kg
vA' = -1.446 m/s [W]
Therefore, the final velocity of glider A is approximately 1.446 m/s [W].