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

answer: good job it's all correct !

explanation:

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.