PHYSICS COLLEGE

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 56 m long that spin at 13 rpm .A. At the tip of a blade, what is the speed?
B. At the tip of a blade, what is the centripetal acceleration?
C. 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 .
D. What force is required to keep a 10 mg water droplet moving in this circular arc?
E. What is the ratio of this force to the weight of a droplet?

Answers

Answer 1
Answer:

A) The speed of the tip of the blade is 76.2 m/s

B) The centripetal acceleration of the tip of the blade is 103.7 m/s^2

D) The force required to keep the droplet moving in circular motion is 0.39 N

E) The ratio of the force to the weight of the droplet is 4.0

Explanation:

A)

We know that the blade of the turbine is rotating at an angular speed of

\omega = 13 rpm

First, we have to convert this angular speed into radians per second. Keeping in mind that

1 rev = 2 \pi

1 min = 60 s

We get

\omega = 13 rpm \cdot (2\pi rad/rev)/(60 s/min)=1.36 rad/s

The linear speed of a point on the blade is given by:

v=\omega r

where

\omega=1.36 rad/s is the angular speed

r is the distance of the point from the axis of rotation

For a point at the tip of the blade,

r = 56 m

Therefore, its speed is

v=(1.36)(56)=76.2 m/s

B)

The centripetal acceleration of a point in uniform circular motion is given by

a=(v^2)/(r)

where

v is the linear speed

r is the distance of the point from the axis of rotation

In this problem, for the tip of the blade we have:

v = 76. 2 m/s is the speed

r = 56 m is the distance from the axis of rotation

Substituting, we find the centripetal acceleration:

a=((76.2)^2)/(56)=103.7 m/s^2

D)

The force required to keep the 10 mg water droplet in circular motion on the dog's fur is equal to the centripetal force experienced by the droplet, therefore:

F=m(v^2)/(r)

where

m is the mass of the droplet

v is the linear speed

r is the distance from the centre of rotation

The data in this problem are

m = 10 mg = 0.010 kg is the mass of the droplet

v = 2.5 m/s is the linear speed

r = 16 cm = 0.16 m is the radius of the circular path

Substituting,

F=(0.010)(2.5^2)/(0.16)=0.39 N

E)

The weight of the droplet is given by

F_g = mg

where

m = 10 mg = 0.010 kg is the mass of the droplet

g=9.8 m/s^2 is the acceleration of gravity

Substituting,

F_g = (0.010)(9.8)=0.098 N

The force that keeps the droplet in circular motion instead is

F = 0.39 N

Therefore, the ratio between the two forces is

(F)/(F_g)=(0.39)/(0.098)=4.0

Learn more about circular motion:

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Answers

Answer:

1391 N

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

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From the question we have

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t or f

Answers

Answer:

Atomic mass is a value that depends on the distribution of an element's isotopes in nature and the masses of those isotopes. Circle the letter of each sentence that is true about a carbon-12 atom. ... Most elements exist as a mixture of two or more isotopes.

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A ball with radius .15 m is rolling with an angular velocity of 6.5 rad/s. (a) What linear distance will the ball roll in 5.0 seconds? The ball then slows down with a linear acceleration of -1.2 rad/s2. (B) How fast will it be rolling rad/s after .65 second? (C) If a piece of gum is stuck on the outer part of the ball, what is its linear speed? (4.9, 5.72, .858)

Answers

Answer:

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Answers

Answer:

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Answer:

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The graph below shows the velocity of a car as it attempts to set a speedrecord.
Velocity vs. Time
1400
1300
1200
1100
1000
4 45
3
1 (s)
At what point is the car the fastest?
A. t = 1.0 s
B. t = 4.2 s
C. t = 3.0 s
D. t = 4.5 s

Answers

From the graph, it is clear that, the velocity is at a time of 1 s is highest. The velocity at 1 second corresponds to 1250 km/hr. Then it decreases with time.

What is velocity - time graph ?

The velocity - time graph shows the change in velocity with respect to time. The velocity is placed in y -axis and time is given in x - axis. The slope of the curve in velocity - time graph gives the acceleration of the object.

Similarly, the position of the object in meter after a t seconds can be determined from the velocity - time graph. It is the rate of change in velocity of the object.

From the graph, it is clear that, the curve has its peak at 1 second. After that the peak descends down. Hence, the maximum velocity of the car is at a time of 1 second at which the velocity is 1250 km/hr.

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Answers

Answer:

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Explanation:

Take down to be positive.  Given:

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Find: v

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v² = (0 m/s)² + 2 (9.8 m/s²) (19 m)

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