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Answer :
Final answer:
The total resistive force against the car, boat, and trailer is 910 N. The force experienced in the hitch between the car and the trailer is 728 N.
Explanation:
This is a classic problem that involves applying Newton's second law and the concept of net force. Newton's second law states that Force = mass * acceleration. Let's begin with the first part of the question.
Given that the car has a mass of 1100 kg and it accelerates at 0.550 m/s2, and uses a force of 1900 N, we realize that this force is not just accelerating the car, but also overcoming some resistance. The total force exerted by the car is the sum of the force to overcome the resistance and the force to accelerate both the car and the trailer. We calculate this total force as follows:
Force_moving = (Mass_car + Mass_trailer) * Acceleration
Force_moving = (1100 kg + 700 kg) * 0.550 m/s2
Force_moving = 990 N
The resistive force then is the difference between the force the car exerts on the road and the force needed to move: Force_resistance = Force_exerted – Force_moving = 1900 N – 990 N = 910 N
In the second part of the question, we’re asked to figure out the force in the hitch between the car and the trailer, if 80% of the resisting forces are experienced by the boat and trailer. We simply take 80% of the resisting force:
Force_hitch = 0.80 * Force_resistance = 0.80 * 910 N = 728 N
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Final answer:
The total resisting force to the motion of the car, boat, and trailer is 910N. The force in the hitch between the car and the trailer, experiencing 80% of the resisting force, is 728N.
Explanation:
The subject of this question pertains to Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
(a) We can use this equation to calculate the total a total force that resists the motion of the car, boat, and trailer: F = ma. Here, F is the net force, m is the total mass (car + boat + trailer), and a is the acceleration. Plugging in the given values (F = (1100kg + 700kg) * 0.550m/s²), we find the net force is 990 N. Since the car is exerting a force of 1900 N, the force resisting the motion can be found by subtracting this net force from the force exerted by the car (1900N - 990N), which gives 910 N.
(b) If 80% of the resisting forces are experienced by the boat and trailer, then the force on the hitch would be 80% of the total resisting force, i.e., 0.8 * 910 N = 728 N.
Learn more about Newton's Second Law of Motion here:
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