Bellwork 5.2 A 1000 kg train car moving at 8m/s collides with a 3000 kg stationary train car Assuming they move off together after the collision, at what velocity will they have? p=mv Mar 4.2025

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision must be equal to the total momentum after the collision.<br /><br />Given information:<br />- Mass of the first train car (m1) = 1000 kg<br />- Velocity of the first train car (v1) = 8 m/s<br />- Mass of the second train car (m2) = 3000 kg<br />- Velocity of the second train car (v2) = 0 m/s (stationary)<br /><br />The formula for momentum is:<br />p = m × v<br /><br />Step 1: Calculate the total momentum before the collision.<br />Total momentum before the collision = (m1 × v1) + (m2 × v2)<br />Total momentum before the collision = (1000 kg × 8 m/s) + (3000 kg × 0 m/s)<br />Total momentum before the collision = 8000 kg·m/s<br /><br />Step 2: Calculate the total momentum after the collision.<br />Since the train cars move off together after the collision, their combined momentum must be equal to the total momentum before the collision.<br />Total momentum after the collision = (m1 + m2) × v<br />8000 kg·m/s = (1000 kg + 3000 kg) × v<br />8000 kg·m/s = 4000 kg × v<br />v = 8000 kg·m/s / 4000 kg<br />v = 2 m/s<br /><br />Therefore, the velocity at which the train cars will move off together after the collision is 2 m/s.