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Answer :
Final answer:
The force exerted by the trailer on the car is calculated using Newton's Second Law of Motion and considering both the mass of the car and trailer along with the given acceleration. Since action and reaction forces are equal and opposite, the force exerted by the trailer on the car is equal to the total force required to accelerate the system, which is 2564.8 N.
Explanation:
To find the force exerted by the trailer on the car, we can use Newton's Second Law of Motion, which states that F = ma, where F is the force applied to an object, m is the mass of the object, and a is the acceleration of the object. However, if frictional forces are negligible as stated, and we are ignoring air drag, the force the car exerts on the trailer will be the same as the force the trailer exerts on the car due to Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
Since the acceleration of the system (car and trailer) is 2.29 m/s², we can calculate the total force needed to accelerate the entire system by adding the mass of the car (620 kg) and the trailer (500 kg) to get the total mass (1120 kg), and then multiplying by the acceleration:
Force required = (Mass of car + Mass of trailer) x Acceleration = (620 kg + 500 kg) x 2.29 m/s² = 1120 kg x 2.29 m/s² = 2564.8 N
The force exerted by the trailer on the car is, therefore, 2564.8 N in the opposite direction of the car's acceleration, fulfilling Newton's Third Law of Motion for equal and opposite forces.
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