Two masses, m1= 1 kg and m2 = 2kg, collide. the first mass has a velocity of .95 m/s east, then 50 degrees NE. The second mass is stationary and then moves off 40 degrees SE. What are the velocities of the two masses after the collision?
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Find the initial momentum of the system:
The initial momentum of the system is the sum of the individual momenta of the masses. The momentum (p) is calculated as mass (m) multiplied by velocity (v).
For m1 (1 kg):
Initial momentum = m1 * v1
= 1 kg * 0.95 m/s (east)
= 0.95 kg⋅m/s (east)
For m2 (2 kg):
Initial momentum = m2 * v2
= 2 kg * 0 m/s (since it is initially stationary)
= 0 kg⋅m/s
The total initial momentum of the system is the vector sum of the individual momenta:
Total initial momentum = Σ(initial momentum of each mass)
= p1 + p2
= 0.95 kg⋅m/s (east) + 0 kg⋅m/s
= 0.95 kg⋅m/s (east)
2. Find the final momentum of the system:
Since the masses collide, the total momentum before and after the collision remains the same (conservation of momentum).
Therefore, the total final momentum of the system after the collision is equal to the initial momentum, i.e., 0.95 kg⋅m/s (east).
3. Find the final velocities of the masses:
The final velocities of the masses can be obtained by dividing the final momentum by their respective masses.
For m1:
Final momentum of m1 = Final velocity of m1 * m1
0.95 kg⋅m/s (east) = Final velocity of m1 * 1 kg
Final velocity of m1 = 0.95 m/s (east)
For m2:
Final momentum of m2 = Final velocity of m2 * m2
0.95 kg⋅m/s (east) = Final velocity of m2 * 2 kg
Final velocity of m2 = 0.475 m/s (east)
Therefore, the final velocities of m1 and m2 after the collision are:
m1: 0.95 m/s (east)
m2: 0.475 m/s (east)