A 1000 kg car is pushing an out-of-gear 2000 kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push horizontally against the ground with a force of 4500 N. Rolling friction can be neglected. What is the magnitude of the force of the car on the truck?

검증된 단계별 안내

Step 1: Start by identifying the total system mass. The car has a mass of 1000 kg, and the truck has a mass of 2000 kg. Therefore, the total mass of the system is the sum of the two: \( m_{\text{total}} = 1000 \; \text{kg} + 2000 \; \text{kg} = 3000 \; \text{kg} \).

Step 2: Use Newton's Second Law of Motion, \( F = ma \), to calculate the acceleration of the system. The net force acting on the system is the force exerted by the car's drive wheels, \( F = 4500 \; \text{N} \). The acceleration of the system is given by \( a = \frac{F}{m_{\text{total}}} \). Substitute the values: \( a = \frac{4500}{3000} \; \text{m/s}^2 \).

Step 3: Focus on the interaction between the car and the truck. The force of the car on the truck is the same as the force required to accelerate the truck alone. Use Newton's Second Law again, \( F_{\text{car on truck}} = m_{\text{truck}} \cdot a \), where \( m_{\text{truck}} = 2000 \; \text{kg} \) and \( a \) is the acceleration calculated in Step 2.

Step 4: Substitute the values into the equation from Step 3: \( F_{\text{car on truck}} = 2000 \cdot a \). Use the acceleration value from Step 2 to complete the calculation.

Step 5: Conclude that the magnitude of the force of the car on the truck is equal to the force required to accelerate the truck at the same rate as the system. This force is determined by the truck's mass and the system's acceleration.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law can be expressed with the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In this scenario, understanding how the forces interact between the car and the truck is crucial for determining the force exerted by the car on the truck.

Force Interaction

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that when the car exerts a force on the truck, the truck exerts an equal force back on the car. This concept is essential for analyzing the forces at play in the system, particularly in understanding how the car's force affects the truck's motion.

System of Objects

In this problem, the car and truck can be considered as a single system. The total mass of the system affects how the forces are distributed and how the system accelerates. By treating the car and truck together, we can apply Newton's laws to find the force exerted by the car on the truck, taking into account the combined mass and the force applied by the car.