On an air track, a 403.0 glider moving to the right at 1.70 collides elastically with a 500.5 glider moving in the opposite direction at 3.00 .
1. Find the velocity of first glider after the collision.
2.
Find the velocity of second glider after the collision.
M1 = 0.403kg, V1 = 1.70 m/s.
M2 = 0.500kg, V2 = -3.0 m/s.
Conservation of Momentum:
M1*V1 + M2*V2 = M1*V3 + M2*V4.
0.403*1.7 + 0.50*(-3.0) = 0.403*V3 + 0.5*V4,
0.6851 - 1.50 = 0.403*V3 + 0.50*V4
Eq1: 0.403*V3 + 0.50*V4 = -0.815.
Conservation of Kinetic Energy Eq:
1. V3 = (V1(M1-M2) + 2M2*V2)/(M1+M2).
V3 = (1.7(0.403-0.5) + 1*(-3))/(0.403+0.5) = -3.50 m/s = Velocity of first glider.
2. In Eq1, replace V3 with (-3.50) and solve for V4.
To find the velocity of the gliders after the collision, we can use the principles of conservation of momentum and kinetic energy.
1. Find the velocity of the first glider after the collision:
a) First, let's find the initial momentum of the system. Momentum (p) is given by the product of mass (m) and velocity (v): p = m * v.
For the first glider (m1 = 403.0 g), the initial momentum is: p1_initial = m1 * v1_initial.
b) For the second glider (m2 = 500.5 g), since it is moving in the opposite direction, its initial momentum is: p2_initial = m2 * v2_initial.
c) The total initial momentum of the system before the collision is the sum of the individual momenta: p_initial_total = p1_initial + p2_initial.
d) According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, p_initial_total = p_final_total.
e) Let's assume the final velocities of the gliders after the collision are v1_final for the first glider and v2_final for the second glider.
Using the given information, we can write the equation for conservation of momentum:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final.
Substituting the given masses and velocities, and solving for v1_final will give us the answer.
2. Find the velocity of the second glider after the collision:
Using the same principle of conservation of momentum, we can rearrange the equation to solve for v2_final:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final.
Substituting the given masses and velocities, and solving for v2_final will give us the answer.