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An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f=bv. Assume that b=15 kg/s and m=50kg. Does your answer to part (a) depend on the intial speed of the object? Explain.

User Rida
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Final answer:

Yes, the answer to part (a) does depend on the initial speed of the object since the air resistance, which is proportional to the object's speed, affects the net force and therefore the net acceleration of the object.

Step-by-step explanation:

The force of air resistance which is proportional to the speed of the object can be represented as f = bv, where b is a constant and v is the speed. Given that b is 15 kg/s and m is 50 kg, the initial speed of the object does indeed affect the air resistance experienced as the resistance force is directly proportional to the speed at which the object falls. As the speed increases, the magnitude of the frictional force of air resistance increases which in turn affects the net acceleration of the object. According to Newton's second law, the acceleration of an object is the net force divided by the mass (a = Fnet/m). If we consider the gravitational force acting downwards as w = mg and air resistance acting upwards, then the net force acting on the falling object is w - bv, and the acceleration can be affected by the initial speed since it affects v over time.

User Yury Imashev
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Final answer:

The answer to the question does not depend on the initial speed of the object.

Step-by-step explanation:

No, the answer to the question does not depend on the initial speed of the object. The statement given in the question is that the frictional force of air resistance is approximately proportional to the speed of the object, denoted as f=bv, where b=15 kg/s and m=50kg. Since b is a constant value and the initial speed is not mentioned in the question, the answer does not depend on the initial speed. The magnitude of the frictional force will vary as the object falls, but it will always be proportional to the speed of the object.

User Birophilo
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