A 10 kg mass moving at 6 m/s strikes a stationary 2 kg mass in an elastic collision. Determine the velocity of each after the collision.
10(6)+2(0)=(10)Vf1+(2)Vf2
60=(10)Vf1+(2)Vf2
To solve for the velocities of each mass after the collision, we can use the principle of conservation of momentum.
The equation for conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Momentum = mass × velocity
The momentum before the collision is given by:
Initial momentum = (mass1 × velocity1) + (mass2 × velocity2)
= (10 kg × 6 m/s) + (2 kg × 0 m/s)
= 60 kg·m/s
The momentum after the collision is given by:
Final momentum = (mass1 × velocity1') + (mass2 × velocity2')
According to the principle of conservation of momentum, the initial and final momentum must be equal, so we have the equation:
Initial momentum = Final momentum
Substituting the known values:
60 kg·m/s = (10 kg × Vf1) + (2 kg × Vf2)
Now we need to solve this equation to determine the final velocities, Vf1 and Vf2.
Since we have two unknowns and only one equation, we need to consider additional information provided in the problem statement. The collision is said to be elastic, which means that both momentum and kinetic energy are conserved.
The equation for conservation of kinetic energy states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Kinetic energy = (1/2) × mass × velocity^2
The kinetic energy before the collision is given by:
Initial kinetic energy = (1/2) × mass1 × velocity1^2 + (1/2) × mass2 × velocity2^2
= (1/2) × 10 kg × (6 m/s)^2 + (1/2) × 2 kg × (0m/s)^2
= 180 J
The kinetic energy after the collision is given by:
Final kinetic energy = (1/2) × mass1 × velocity1'^2 + (1/2) × mass2 × velocity2'^2
Since the collision is elastic, the initial and final kinetic energy are equal, so we have the equation:
Initial kinetic energy = Final kinetic energy
Substituting the known values:
180 J = (1/2) × 10 kg × (Vf1)^2 + (1/2) × 2 kg × (Vf2)^2
Now we have two equations, 60 kg·m/s = (10 kg × Vf1) + (2 kg × Vf2) and 180 J = (1/2) × 10 kg × (Vf1)^2 + (1/2) × 2 kg × (Vf2)^2.
To solve these equations, you can either use a system of equations solver or solve them manually by substitution or elimination. By solving these equations, you can determine the values of Vf1 and Vf2, which represent the final velocities of the two masses after the collision.