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 = 14 kg/s and m = 41 kg.
(a) What is the terminal speed that the object reaches while falling?
1 m/s(b)
Does your answer to part (a) depend on the initial speed of the object?
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To find the terminal speed of the object, we can set up an equation balancing the gravitational force and the air resistance force.
The gravitational force on the object can be calculated using the equation:
F_gravity = m * g
where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The air resistance force can be calculated using the equation:
F_air = b * v
where b is the proportionality constant and v is the speed of the object.
At terminal speed, the object stops accelerating and reaches a constant velocity. This means that the net force on the object is zero, so the forces due to gravity and air resistance must be equal:
F_gravity = F_air
Therefore, we can set up the equation:
m * g = b * v
Plugging in the given values:
m = 41 kg
b = 14 kg/s
g = 9.8 m/s^2
41 kg * 9.8 m/s^2 = 14 kg/s * v
Simplifying the equation:
402.8 = 14v
To find the terminal speed, we solve for v:
v = 402.8 / 14 ≈ 28.77 m/s
Therefore, the terminal speed that the object reaches while falling is approximately 28.77 m/s.
Now, let's address part (b) of the question. The terminal speed of the object does not depend on the initial speed of the object. The only factors that affect the terminal speed are the mass of the object and the air resistance force, which is determined by the speed of the object. The initial speed of the object may impact how quickly it reaches the terminal speed, but it does not affect the value of the terminal speed itself.