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 = 10 kg/s and m = 56 kg.
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To find the magnitude of the air resistance force acting on the object, we can use the equation:
f = bv
Here, f represents the force of air resistance, b is a constant, and v is the speed of the object. Given that b = 10 kg/s, we can substitute this value into the equation:
f = 10v
Now, we need to determine the speed of the object. Since the object is falling under the influence of gravity, its speed will increase as it falls. The relationship between time (t) and speed (v) for an object in free fall can be described by the equation:
v = gt
Where g represents the acceleration due to gravity, which is approximately equal to 9.8 m/s^2. However, in this case, we are not given the time but the mass (m) of the object, which is 56 kg.
To find the speed of the falling object, we can use the concept of terminal velocity. Terminal velocity is the maximum speed reached by an object falling through a fluid when the upward force of air resistance equals the downward force of gravity. At terminal velocity, the net force acting on the object becomes zero, resulting in a constant speed.
To calculate the terminal velocity, we set the net force equal to zero:
mg - bv = 0
Substituting the given values for m and b:
56(9.8) - 10v = 0
Rearranging the equation:
550.8 = 10v
Finally, solving for v:
v = 550.8 / 10
v = 55.08 m/s
Now that we have the speed of the object, we can substitute this value back into the equation for air resistance:
f = 10v
f = 10(55.08)
f ≈ 550.8 N
Therefore, the magnitude of the air resistance force acting on the object is approximately 550.8 N.