The crash test technicians gave you the following data from their experiments. They crashed each of these cars into a 1200 kg car accelerating at 3 m/s^2. Would these cars move forward or backward when they backed into the test car? Explain how you get your answers.
To determine whether the cars would move forward or backward when they backed into the test car, we need to analyze the forces acting on them during the collision.
When a car collides with another car, the force experienced by both cars is equal and opposite due to Newton's third law of motion. In this case, the force exerted on each car is the same, as they are crashing into the same test car with the same acceleration.
Assuming the initial velocity of all cars is zero, we can calculate the net force acting on each car using Newton's second law:
Net force = mass × acceleration
Let's consider the four scenarios provided:
1. Car A: Net force = mass of Car A × acceleration
2. Car B: Net force = mass of Car B × acceleration
3. Car C: Net force = mass of Car C × acceleration
4. Car D: Net force = mass of Car D × acceleration
If the net force on a car is positive, it means the car will move forward when it backs into the test car. If the net force is negative, the car will move backward.
So, we need to calculate the net forces for all the cars.
Assuming:
Mass of Car A = 1200 kg
Mass of Car B = 1000 kg
Mass of Car C = 1500 kg
Mass of Car D = 900 kg
Acceleration = 3 m/s^2
1. Car A: Net force = 1200 kg × 3 m/s^2 = 3600 N
2. Car B: Net force = 1000 kg × 3 m/s^2 = 3000 N
3. Car C: Net force = 1500 kg × 3 m/s^2 = 4500 N
4. Car D: Net force = 900 kg × 3 m/s^2 = 2700 N
Based on the net forces calculated, we can determine the direction of movement:
1. Car A: The net force is positive (3600 N), indicating that it will move forward when backed into the test car.
2. Car B: The net force is positive (3000 N), indicating that it will move forward when backed into the test car.
3. Car C: The net force is positive (4500 N), indicating that it will move forward when backed into the test car.
4. Car D: The net force is positive (2700 N), indicating that it will move forward when backed into the test car.
Therefore, all the cars (A, B, C, and D) will move forward when they back into the test car, as the net forces acting on them are positive.
To determine whether the cars would move forward or backward when they backed into the test car, we need to consider the concept of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In this case, the action is the crash, and the reaction is the force exerted on each car involved in the crash. According to Newton's third law, the force exerted by the 1200 kg car is equal in magnitude but opposite in direction to the force exerted on the crashed cars.
Since the 1200 kg car is accelerating at 3 m/s^2, we can calculate the force exerted on this car using Newton's second law of motion: force = mass × acceleration.
Force exerted on the 1200 kg car = (mass of the 1200 kg car) × (acceleration of the 1200 kg car)
Force exerted on the 1200 kg car = (1200 kg) × (3 m/s^2)
Force exerted on the 1200 kg car = 3600 N (Newtons)
Since the force exerted by the crashed cars is equal in magnitude but opposite in direction to the force exerted on the 1200 kg car (3600 N), we can conclude that the crashed cars would move backward when they back into the test car.