A .001 kg bead slides without friction around a loop-the-loop. The bead is released from a height of 20.6 m from the bottom of t
1 answer:
Answer:
11.37 m/s
Explanation:
We are given;
Mass; m = 0.001 kg
Initial velocity; v1 = 0 m/s (since it was released from rest)
Initial height; h1 = 20.6m
From the attached image of the bead in the loop, we can see that height at A; h2 = twice the radius = 2R = 2 × 7 = 14 m
g = 9.8
To solve for the speed at point, we will use formula for conservation of energy. Thus;
½m(v1)² + mgh1 = ½m(v2)² + mgh2
Divide through by m to get;
½(v1)² + gh1 = ½(v2)² + gh2
Plugging in the relevant values;
½(0²) + (9.8 × 20.6) = ½(v2)² + (9.8 × 14)
Rearranging, we have;
½(v2)² = ½(0²) + (9.8 × 20.6) - (9.8 × 14)
Simplifying, we have;
½(v2)² = 64.68
Multiply both sides by 2 to get;
(v2)² = 2 × 64.68
(v2)² = 129.36
v2 = √129.36
v2 = 11.37 m/s
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Complete Question
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick
Answer:
The largest total area of the oil slick
Explanation:
From the question we are told that
The volume of oil the escaped is
The refractive index of oil is
The refractive index of water is
The wavelength of the light is
Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as
Where is the order of interference of the light and it value ranges from 1, 2, 3,...n
It is usually take as 1 unless stated otherwise by the question
substituting value
The are can be mathematically evaluated as
Substituting values
Answer:
Refer to the attachment!~
