To determine the tension force in the coupling between the middle car and the engine car of the train, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). In this case, we need to analyze the forces acting on the middle car and the engine car separately.
Understanding the Components of the Train
The train consists of three parts:
- Caboose: 1000 kg
- Middle Car: 2000 kg
- Engine Car: 2000 kg
Calculating the Total Mass
The total mass of the train can be calculated as follows:
Total Mass = Mass of Caboose + Mass of Middle Car + Mass of Engine Car
Total Mass = 1000 kg + 2000 kg + 2000 kg = 5000 kg
Finding the Total Force Acting on the Train
Using the acceleration of the train, we can find the total force required to accelerate the entire train:
Total Force = Total Mass × Acceleration
Total Force = 5000 kg × 5 m/s² = 25000 N
Analyzing the Forces on the Middle Car
Next, we need to focus on the forces acting specifically on the middle car. The middle car has a mass of 2000 kg and is also accelerating at 5 m/s². The force acting on the middle car can be calculated as:
Force on Middle Car = Mass of Middle Car × Acceleration
Force on Middle Car = 2000 kg × 5 m/s² = 10000 N
Understanding the Tension Force
The tension force in the coupling between the middle car and the engine car must provide the necessary force to accelerate the middle car. Since the middle car is being pulled by the engine car, the tension force must equal the force required to accelerate the middle car. Therefore, the tension force in the coupling between the middle car and the engine car is:
Tension Force = Force on Middle Car
Tension Force = 10000 N
Final Answer
Thus, the tension force in the coupling between the middle car and the engine car is 10000 N, which corresponds to option (4).
