Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. a turbine has blades 59m long that spin at13rpm .

at the tip of a blade, what is the speed?
at the tip of a blade, what is the centripetal acceleration?
a big dog has a torso that is approximately circular, with a radius of 16cm . at the midpoint of a shake, the dog's fur is moving at a remarkable 2.5m/s .
what force is required to keep a 10 mg water droplet moving in this circular arc?
what is the ratio of this force to the weight of a droplet?

speed and acceleration of the turbine V = 80.24 m/s   and a = 109.1 m/s²

Explanation:

The wind turbine describes a circular motion, with constant angular velocity, we can find the speed with the equation

                     V = x / t

Where x is the distance traveled which is the length of the circle (X = 2πr) and time is the time in a revolution, which in this case is called the period

                    t = 60/13  

                    t = 4.62 s

                    x = 2 p1 59

                    x = 370.71 m

                    V = 370.1 / 4.62

                    V = 80.24 m / s

The centripetal acceleration is given by the equation

                   a = V² / r

                   a = 80.24²/59

                   a = 109.1 m / s²

The second part of the exercise seems totally independent

The dog r = 16cm with a speed of 2.5 m/s, ask us the centripetal force

                  F = m a

                  F = m (v² / r)

                  m = 10 mg (1g / 1000mg) 1 Kg / 1000 g) = 1 10⁻⁵ Kg

                  r = 16 cm (1m / 100cm) = 16 10⁻² m

                 F = 1 10⁻⁵ 2.5²/16 10⁻²

                 F = 3.91 10⁻² N

Let's calculate the relationship between the force and the weight of the drop

                 F / W = 3.91 10⁻² (1 10⁻⁵ 9.8)

                 F / W = 3.99 10 ²

See that the force of the shake is approximately 400 times greater than the weight of the drop

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.