A rectangular neoprene sheet has width W = 1.00 m and length L = 4.00 m. The two shorter edges are affixed to rigid steel bars that are used to stretch the sheet taut and horizontal. The force applied to either end of the sheet is F = 81.0 N. The sheet has a total mass M = 4.00 kg. The left edge of the sheet is wiggled vertically in a uniform sinusoidal motion with amplitude A = 10.0 cm and frequency f = 1.00 Hz. This sends waves spanning the width of the sheet rippling from left to right. The right side of the sheet moves upward and downward freely as these waves complete their traversal.
(A) Derive an expression for the velocity with which the waves move along the sheet. Express your answer in terms of the variables F, L, and M.
(B) What is the value of this speed for the specified choices of these parameters? Express your answer with the appropriate units.

(a)

(b)

Explanation:

(a)

The speed of the wave depends on the type of the material. Here we have neoprene sheet so the speed of the wave will depend on the linear density of neoprene sheet. Linear Density is defined as Mass per unit length of the material (as materials of same type can have different thickness). The symbol used for the Linear Density is .

μ = Mass of the sheet / Length of the sheet

The speed of the wave in such material can be be found by using the equation:

(where v is speed)

The equation can be rearranged:

v =

so,

v = sqrt(F/μ)

v = sqrt(F/ (M/L))

v = (answer)

(b)

Putting the values

F = 81 N

M = 4kg

L = 4m

v =

v = 9m/s

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.