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photoshop1234 [79]
3 years ago
14

Problem 8.8. A rod of length L and mass m is held in a vertical position on a rough horizontal surface (Fig. P.8.8). The rod is

then slightly displaced from the vertical unstable equilibrium position (Fig. P.8.8a) and let go. The rod will rotate clockwise around point A without slip (Fig.P.8.8b), but eventually the slipping must take place before the horizontal position is reached (Fig. P.8.8c). Determine the angular velocity of the rod as a function of its angle of inclination with the vertical axis before the slip takes place. At which value of theta does the slip takes place?
Mathematics
1 answer:
musickatia [10]3 years ago
8 0

Answer:

ω = √((3g/L)*(1 - Cos θ))

Step-by-step explanation:

We need to apply the Principle of Conservation of mechanical energy as follows

Ei = Ef    ⇒ Ki + Ui = Kf + Uf

In the vertical position

ωi = 0 ⇒ Ki = 0

yi = L/2 ⇒ Ui = m*g*L/2

We can get the rotational inertia I using the formula

I = m*L²/3

then

Kf = I*ω²/2 = (m*L²/3)*ω²/2 = m*L²*ω²/6

Now, we obtain the potential energy Uf as follows

Uf = m*g*y

where

y = (L/2)*Cos θ

⇒ Uf = m*g*(L/2)*Cos θ

Now, we have

Ui = Kf + Uf

⇒ m*g*L/2 = (m*L²*ω²/6) + (m*g*(L/2)*Cos θ)

⇒ ω² = (3g/L)*(1 - Cos θ)

⇒ ω = √((3g/L)*(1 - Cos θ))

We need to know the coefficient of static friction in order to get the value of theta where slip takes place.

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A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of
Studentka2010 [4]

Answer:

The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099

Step-by-step explanation:

A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of  8 dollars.

Mean = \mu = 87

Standard deviation = \sigma = 8

We are supposed to find proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars i.e.P(104.60<x<108.20)

Z=\frac{x-\mu}{\sigma}

At x = 104.60

Z=\frac{104.60-87}{8}

Z= 2.2

At x=108.20

Z=\frac{108.20-87}{8}

Z= 2.65

Refer the z table for p value :

P(x<108.20)-P(x<104.60)=P(Z<2.65)-P(Z<2.2)=0.9960-0.9861=0.0099

Hence The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099

4 0
3 years ago
Two airplanes leave the airport. Plane A departs at a 44° angle from the runway, and plane B departs at a 40° angle from the run
lawyer [7]

Answer: Answer:

Plane B was farthest away from the airport

Step-by-step explanation:

"This question requires you to visualize the run way as the horizontal distance to be covered, the height from the ground as the height gained by the plane after take of and the distance from the airport as the displacement due to the angle of take off.

In plane A

The take-off angle is 44° and the height gained is 22 ft.

Apply the relationship for sine of an angle;

Sine Ф°= opposite side length÷hypotenuse side length

The opposite side length is the height gained by plane which is 22 ft

The angle is 44° and the distance the plane will be away from the airport after take-off will be represented by the value of hypotenuse

Applying the formula

sin Ф=O/H where O=length of the side opposite to angle 44° and H is the hypotenuse

In plane B

Angle of take-off =40°, height of plane=22miles finding the hypotenuse

Solution

After take-off and reaching a height of 22 ft from the ground, plane A will be 31.67 miles from the airport

After take-off and reaching a height of 22 ft from the ground, plane B will be 34.23 miles away from the airport."

Excerpt from Brainly

3 0
2 years ago
Read 2 more answers
Help me please <br><br> will get rewared brainly if correct answer
larisa [96]

Well, split it into 3 shapes

21 x 10 = 210

3 x 6 = 18

2 x 6 = 12

210 + 18 + 12 = 240 square cm

imahe for more context

plzzz give me brainliest

5 0
3 years ago
Which of the following will be equal to 1⁄4?
docker41 [41]

Answer:

C - 100% of 0.25

Step-by-step explanation:

This answer is basically the same as 25% of 100, just worded differently to confuse you.

25 is 1/4th of 100, so this should be the answer. :)

If you're curious of what the other answers amount to:

One hundredth of 250 = 2.5

50% of 5 = 2.5

40% of 1 = 0.4

6 0
3 years ago
What is the equation in point slope form of the line that passes through (0,5) and (-2,11)
tester [92]
The point slope form equation is 3x + y = -35
7 0
3 years ago
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