A North-going Zak has a mass of 50 kg and is traveling at 4 m/s. A South -going Zak has a mass of 40 kg and is traveling at 5 m/s. If they get stuck together after the collision, what is their final velocity?
system momentum is conserved
they have equal and opposite momenta before the collision
To find the final velocity after the collision, we need to use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of the North-going Zak as m1 = 50 kg and its velocity as v1 = 4 m/s. The mass of the South-going Zak will be denoted as m2 = 40 kg and its velocity as v2 = -5 m/s (negative sign indicates the opposite direction).
The total momentum before the collision is given by:
Total momentum before = m1 * v1 + m2 * v2
Plugging in the values:
Total momentum before = (50 kg * 4 m/s) + (40 kg * -5 m/s)
= (200 kg*m/s) + (-200 kg*m/s)
= 0 kg*m/s
Since the Zak's stick together after the collision, their masses combine, so we have a single mass of 50 kg + 40 kg = 90 kg. Let's denote their final velocity after the collision as v_final.
The total momentum after the collision is given by:
Total momentum after = (m1 + m2) * v_final
Using the principle of conservation of momentum, we can equate the total momentum before and after the collision:
Total momentum before = Total momentum after
0 kg*m/s = (50 kg + 40 kg) * v_final
Simplifying the equation, we find:
0 kg*m/s = 90 kg * v_final
To solve for v_final, divide both sides by 90 kg:
0 kg*m/s / 90 kg = v_final
Therefore, their final velocity after the collision is 0 m/s.
To find their final velocity after the 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 calculated by multiplying its mass by its velocity. So, the momentum of the North-going Zak before the collision is given by:
Momentum = mass × velocity = 50 kg × 4 m/s = 200 kg·m/s
Similarly, the momentum of the South-going Zak before the collision is:
Momentum = mass × velocity = 40 kg × 5 m/s = 200 kg·m/s
Since the two Zak's get stuck together after the collision, their final mass will be the sum of their individual masses, which is 50 kg + 40 kg = 90 kg.
Let's denote the final velocity of the combined Zak as Vf. By the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
Total Momentum before collision = Total Momentum after collision
(50 kg × 4 m/s) + (40 kg × 5 m/s) = 90 kg × Vf
Simplifying the equation:
(200 kg·m/s) + (200 kg·m/s) = 90 kg × Vf
400 kg·m/s = 90 kg × Vf
Finally, solving for Vf:
Vf = 400 kg·m/s / 90 kg
Vf ≈ 4.44 m/s
Therefore, the final velocity of the combined Zak after the collision is approximately 4.44 m/s.