1. To determine the force the train exerts on the car, we use Newton's second law: F = ma. The mass of the car is 250 kg and the acceleration is 0.6 m/s². Therefore, F = 250 kg × 0.6 m/s² = 150 N. The train exerts a force of 150 N on the car.
2. The force the car exerts on the train is equal in magnitude and opposite in direction to the force the train exerts on the car, according to Newton's third law. Thus, the car exerts a force of 150 N on the train.
3. The acceleration of the train is calculated using Newton's second law: a = F/m. The force is 150 N and the mass of the train is 2500 kg. Therefore, a = 150 N / 2500 kg = 0.06 m/s².
4. The distance the train travels can be found using the kinematic equation: d = (v² - u²) / (2a), where v is the final velocity (2 m/s), u is the initial velocity (0 m/s), and a is the acceleration (0.06 m/s²). So, d = (2² - 0²) / (2 × 0.06) = 4 / 0.12 = 33.33 m. The train travels 33.33 meters.
5. The time taken to travel this distance is found using the equation: t = (v - u) / a. So, t = (2 - 0) / 0.06 = 2 / 0.06 = 33.33 s. The train takes 33.33 seconds.
6. The momentum of the train is given by p = mv. The mass of the train is 2500 kg and the velocity is 2 m/s. Therefore, p = 2500 kg × 2 m/s = 5000 kg·m/s.
7. The momentum of the car is p = mv. The mass of the car is 250 kg and the velocity is 2 m/s. Therefore, p = 250 kg × 2 m/s = 500 kg·m/s.
8. The total momentum of the system (train + car) is the sum of their individual momenta: 5000 kg·m/s + 500 kg·m/s = 5500 kg·m/s.
9. The force the train exerts on the car is 150 N, as calculated in step 1.
10. The force the car exerts on the train is 150 N, as calculated in step 2.
11. The total momentum of the system is 5500 kg·m/s, as calculated in step 8.
12. The force the train exerts on the car is 150 N, as calculated in step 1.
13. The force the car exerts on the train is 150 N, as calculated in step 2.
14. The total momentum of the system is 5500 kg·m/s, as calculated in step 8.
15. The total momentum of the system is conserved because there are no external forces acting on the system. The internal forces (the force between the train and the car) are equal and opposite, so they do not change the total momentum.
16. The total momentum of the system is 5500 kg·m/s, as calculated in step 8.
17. The total momentum of the system is conserved because there are no external forces acting on the system. The internal forces (the force between the train and the car) are equal and opposite, so they do not change the total momentum.
18. The total momentum of the system is 5500 kg·m/s, as calculated in step 8.
19. The total momentum of the system is conserved because there are no external forces acting on the system. The internal forces (the force between the train and the car) are equal and opposite, so they do not change the total momentum.
20. The total momentum of the system is 5500 kg·m/s, as calculated in step 8.
Parent Tip: Review the logic above to help your child master the concept of physical science motion and forces worksheet answers.
