Answer:
After the elastic collision, the first particle (5 kg) will be moving with a velocity of 2 m/s at an angle of 50 degrees to the left from its original direction of motion. The second particle (8 kg) will come to rest (velocity = 0 m/s).
Step-by-step explanation:
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy for an elastic collision.
Conservation of momentum:
In an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
Conservation of kinetic energy:
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Let's assume the initial velocity of the first particle (mass = 5 kg) is v1 and the final velocity after the collision is u1, and the initial velocity of the second particle (mass = 8 kg) is v2, and the final velocity after the collision is u2.
Step 1: Conservation of momentum
Initial momentum = Final momentum
m1 * v1 + m2 * v2 = m1 * u1 + m2 * u2
Step 2: Conservation of kinetic energy
Initial kinetic energy = Final kinetic energy
(1/2) * m1 * v1^2 + (1/2) * m2 * v2^2 = (1/2) * m1 * u1^2 + (1/2) * m2 * u2^2
Given data:
m1 = 5 kg
v1 = 2 m/s
m2 = 8 kg
v2 = 0 m/s (initially at rest)
Step 3: Calculate the final velocities after the collision (u1 and u2).
Step 4: Calculate the angle of deflection for the first particle.
Let's solve the equations:
Step 1:
5 kg * 2 m/s + 8 kg * 0 m/s = 5 kg * u1 + 8 kg * u2
10 kg m/s = 5u1 + 8u2
Step 2:
(1/2) * 5 kg * (2 m/s)^2 + (1/2) * 8 kg * (0 m/s)^2 = (1/2) * 5 kg * u1^2 + (1/2) * 8 kg * u2^2
10 J = (1/2) * 5 kg * u1^2 + 0 J
Simplifying Step 2:
10 J = (1/2) * 5 kg * u1^2
u1^2 = (10 J) * 2 / 5 kg
u1^2 = 4 J/kg
u1 = √(4 J/kg)
u1 = 2 m/s (velocity of particle 1 after collision)
Step 1 (revisited):
10 kg m/s = 5 * 2 + 8 * u2
10 kg m/s - 10 kg = 8 * u2
u2 = (10 kg m/s - 10 kg) / 8
u2 = 0.0 m/s (velocity of particle 2 after collision)
Step 4:
The angle of deflection is given as 50 degrees from the original direction of motion for particle 1. Since the original direction was 2 m/s to the right, the deflection will be 50 degrees to the left.
Final answer:
After the elastic collision, the first particle (5 kg) will be moving with a velocity of 2 m/s at an angle of 50 degrees to the left from its original direction of motion. The second particle (8 kg) will come to rest (velocity = 0 m/s).