A toy locomotive of mass 420g moving at 30cm s^-1 south collides with a carriage of mass 200g moving at 30cm s^-1 north. If they become couple together, what is their common velocity after the collision?
just preserve momentum:
(420)(-30) + (200)(30) = (420+200)(v)
v = -10.65
To find the common velocity of the toy locomotive and the carriage after the collision, we can apply 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 defined as the product of its mass and velocity. So, we need to calculate the initial momentum of the toy locomotive and the carriage separately, and then find the total momentum.
The initial momentum of an object can be calculated using the formula: momentum = mass × velocity.
For the toy locomotive:
Mass of toy locomotive (m1) = 420g = 0.42kg
Velocity of toy locomotive (v1) = 30cm/s south = -30cm/s (negative because it is in the opposite direction)
Initial momentum of toy locomotive (p1) = m1 × v1 = 0.42kg × (-30cm/s) = -12.6 kg·cm/s
For the carriage:
Mass of carriage (m2) = 200g = 0.2kg
Velocity of carriage (v2) = 30cm/s north = +30cm/s (positive because it is in the same direction)
Initial momentum of carriage (p2) = m2 × v2 = 0.2kg × 30cm/s = 6 kg·cm/s
Now, we can find the total momentum before the collision:
Initial total momentum (p_initial) = p1 + p2 = -12.6 kg·cm/s + 6 kg·cm/s = -6.6 kg·cm/s
After the collision, the toy locomotive and the carriage become coupled together, which means they move with a common velocity.
Let's assume the common velocity after the collision is v_final.
The final momentum of the toy locomotive and the carriage, when coupled together, will be the sum of their masses multiplied by the common velocity: Final momentum (p_final) = (m1 + m2) × v_final
According to the principle of conservation of momentum, p_initial = p_final
Therefore, we have: -6.6 kg·cm/s = (0.42kg + 0.2kg) × v_final
Simplifying the equation: -6.6 kg·cm/s = 0.62kg × v_final
Divide both sides of the equation by 0.62kg: v_final = -6.6 kg·cm/s ÷ 0.62kg ≈ -10.65 cm/s
Hence, the common velocity of the toy locomotive and the carriage after the collision is approximately -10.65 cm/s. The negative sign indicates that the final velocity is in the opposite direction of the initial velocity of the toy locomotive.