Answering the two questions in reverse order:
-- No. I don't need to know how the speed of the person changed before I can answer the question. I can answer it now.
-- The NET work done by the gravitational force is<em> zero</em>.
-- As the person and his girl-friend go up the first half of the wheel, the motor does positive work and gravity does negative work.
-- After they pass the peak at the top and come down the second half of the wheel, the motor does negative work and gravity does positive work, even though the couple may be interested in other things during that time.
-- The total work done by gravity in one complete revolution is zero.
-- The total work done by the motor in one complete revolution is only what it takes to pay back the energy robbed by friction and air resistance.
To find a solution to this problem it is necessary to apply the concepts related to the Reynolds number and its definitions on the type of fluid.
A Reynolds number less than 2000 considers the laminar fluid, while a Reynolds number greater than 4000 is considered a turbulent fluid. (The intermediate between the two values would be a transient fluid)
The mathematical equation that defines the Reynolds number is given by

Where
Density
V= Velocity
D= Diameter
Viscosity
Our values are given as





The velocity can be find through the Discharge equation,
Q = VA
Where
V = Velocity
A = Area
Replacing,


Replacing at the Reynolds equation,



Since Reynolds' number is greater than 4000, then we consider this a turbulent fluid.
Given that:
spring compressed ( x) = 0.2 m
Work (W) = 24 J
determine , spring constant (x)=?
We know hat ,
Work (W) = (1/2). k.x²
24 = 1/2 ( k × 0.2²)
48 = k × 0.2²
<em> k = 1200 N/m</em>
Complete Question
Suppose you hit a steel nail with a 0.500-kg hammer, initially moving at 15.0 m/s and brought to rest in 2.80 mm. How much is the nail compressed if it is 2.50 mm in diameter and 6.00-cm long.What Average force is excreted on the Nail
Answer:

Explanation:
From the question we are told that:
Mass 
Initial Velocity 
Distance 
Diameter 
Length 
Generally the equation for Force is mathematically given by



Answer:
The angle between the red and blue light is 1.7°.
Explanation:
Given that,
Wavelength of red = 656 nm
Wavelength of blue = 486 nm
Angle = 37°
Suppose we need to find the angle between the red and blue light as it leaves the prism


We need to calculate the angle for red wavelength
Using Snell's law,

Put the value into the formula



We need to calculate the angle for blue wavelength
Using Snell's law,

Put the value into the formula



We need to calculate the angle between the red and blue light
Using formula of angle

Put the value into the formula


Hence, The angle between the red and blue light is 1.7°.