a 0.300kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 m/s when it makes a head on collision with a stationary 0.150kg glider.
(a) Find the magnitude and direction of the final velocity of each glider in the collision is elastic.
(b) Find the final kinetic energy of each glider
M1 = 0.30kg, V1 = 0.8 m/s.
M2 = 0.150kg, V2 = 0.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
0.3*0.8 + 0.15*0 = 0.3*V3 + 0.15*V4,
Eq1: 0.3*V3 + 0.15*V4 = 0.24.
Conservation of KE Eq:
V3 = (V1(M1-M2) + 2M2*V2)/(M1+M2).
V3 = (0.8(0.3-0.15) + 0.30*0)/(0.3+0.15) = 0.267 m/s. = Final velocity of M1.
In Eq1, replace V3 with 0.267 and solve for V4:
0.3*0.267 + 0.15*V4 = 0.24.
0.15*V4 = 0.16,
V4 = 1.07 m/s. = Velocity of M2.
Direction: Both gliders are moving to the right.
b. KE1 = 0.5M1*V3^2 = 0.5*0.3*0.267^2 = 0.011 J. = Kinetic energy of M1.
KE2 = 0.5M2*V4^2 = 0.5*0.15*1.07^2 = 0.086 J. = Kinetic energy of M2.
(a) Well, well, we have a glider collision here! In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. So, let's analyze it!
The initial momentum of the first glider (0.300 kg) is given by:
P1_initial = m1 * v1_initial
P1_initial = 0.300 kg * 0.80 m/s
The second glider is initially stationary, so its initial momentum is zero.
Now, after the collision, let the final velocities be v1_final and v2_final for the first and second gliders, respectively.
Since momentum is conserved, we have:
P1_initial + P2_initial = P1_final + P2_final
0.300 kg * 0.80 m/s + 0 = 0.300 kg * v1_final + 0.150 kg * v2_final
Solving the equation, we have:
0.24 kg·m/s = 0.3 kg * v1_final + 0.15 kg * v2_final -----(1)
Now, since it is an elastic collision, kinetic energy is also conserved. So we have:
(1/2) * m1 * v1_initial^2 + (1/2) * m2 * v2_initial^2 = (1/2) * m1 * v1_final^2 + (1/2) * m2 * v2_final^2
(1/2) * 0.300 kg * (0.80 m/s)^2 + (1/2) * 0.150 kg * (0 m/s)^2 = (1/2) * 0.300 kg * v1_final^2 + (1/2) * 0.150 kg * v2_final^2
Simplifying that, we find:
0.096 J = 0.3 kg * v1_final^2 + 0.15 kg * v2_final^2 -----(2)
Now we have a system of two equations with two unknowns (v1_final and v2_final). Time to do some math-chinery to find the final velocities and make everyone happy!
(b) Ah, we are not done yet! Let's find the final kinetic energy of each glider.
The final kinetic energy of the first glider is given by:
K1_final = (1/2) * m1 * v1_final^2
And the final kinetic energy of the second glider is:
K2_final = (1/2) * m2 * v2_final^2
Just plug in the values we've found for v1_final and v2_final, and calculate. Voilà, there you have it!
Now, I don't know about you, but I find it quite exhilarating to witness the aftermath of a glider collision. It's like a dance, but with more physics!
To find the magnitude and direction of the final velocity of each glider in the elastic collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
(a) Find the magnitude and direction of the final velocity:
Before the collision:
Mass of glider 1 (moving): m1 = 0.300 kg
Velocity of glider 1 (moving): v1 = 0.80 m/s
Mass of glider 2 (stationary): m2 = 0.150 kg
Velocity of glider 2 (stationary): v2 = 0 m/s (since it is stationary)
Total momentum before the collision:
Initial momentum = m1 × v1 + m2 × v2
= 0.300 kg × 0.80 m/s + 0.150 kg × 0 m/s
= 0.240 kg•m/s
After the collision, since it is an elastic collision, the total momentum remains the same. Let's assume the final velocities of the gliders are v1' and v2'.
Total momentum after the collision:
Final momentum = m1 × v1' + m2 × v2'
= 0.300 kg × v1' + 0.150 kg × v2'
Since momentum is conserved, the initial momentum is equal to the final momentum:
0.240 kg•m/s = 0.300 kg × v1' + 0.150 kg × v2' (Equation 1)
Additionally, in an elastic collision, both the momentum and the kinetic energy are conserved. We can use this information to solve this problem.
(b) Find the final kinetic energy of each glider:
The kinetic energy of an object is given by the equation: kinetic energy = (1/2) × mass × velocity^2
Before the collision:
Initial kinetic energy of glider 1 (moving):
KE1 = (1/2) × m1 × v1^2
= (1/2) × 0.300 kg × (0.80 m/s)^2
Initial kinetic energy of glider 2 (stationary):
KE2 = (1/2) × m2 × v2^2
= (1/2) × 0.150 kg × (0 m/s)^2
= 0 J (since it's stationary, its kinetic energy is zero)
Total initial kinetic energy:
Initial KE = KE1 + KE2
After the collision, the total kinetic energy remains the same, as it is an elastic collision. Let's assume the final kinetic energies of the gliders are KE1' and KE2'.
Total final kinetic energy:
Final KE = KE1' + KE2'
Since the kinetic energy is conserved, the initial kinetic energy is equal to the final kinetic energy:
Initial KE = Final KE
KE1 + KE2 = KE1' + KE2' (Equation 2)
To solve the system of equations (Equation 1 and Equation 2), we need to find the values of v1', v2', KE1', and KE2'.
and your question is?
you have the conservation of momentum, and the energy conservation. You have two unknowns, and two equations.
find in momentum one velocity in terms of the other, then put that into the second equation and do the algebra. It will be a quadratic.