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Answer :
Final answer:
The force exerted by the trailer on the car is calculated using Newton's second law for the trailer and recognizing action-reaction pairs. With a mass of 500 kg for the trailer and an acceleration of 2.29 m/s², the force exerted by the trailer on the car is 1145 N, which is equal and opposite to the force the car exerts on the trailer. Therefore the correct answer is None of the above.
Explanation:
Since we're looking for the force the trailer exerts on the car, we actually need to find the force the car exerts on the trailer first and recognize that by Newton's third law (action-reaction pairs), this force will be equal in magnitude but opposite in direction to the force the trailer exerts on the car.
First, calculate the total force exerted on the system (car plus trailer) by using the combined mass and the given acceleration:
Ftotal = (mass of car + mass of trailer) × acceleration
Ftotal = (620 kg + 500 kg) × 2.29 m/s²
Ftotal = 1110 kg × 2.29 m/s²
Ftotal = 2541.9 N
This is the net force required to accelerate both the car and the trailer. But we only want the force that the trailer exerts on the car. For that, we need to use the mass of the trailer and the acceleration to find the force on just the trailer:
Ftrailer = mass of trailer × acceleration
Ftrailer = 500 kg × 2.29 m/s²
Ftrailer = 1145 N
This 1145 N is the force the car applies on the trailer, so by Newton's third law, it's also the force the trailer applies on the car but in the opposite direction. Hence, the correct answer is 1145 N.
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