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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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alexandr1967 [171]

Let x represent Holly's score on 7th math quiz.

We have been given that the mean of Holly's first six math quiz scores was 75%. This means that the average on 1st 6 math quizzes is 75.

To find the total scores on 1st 6 math quizzes, we will multiply 75 by 6 that is 75\times 6 =450.

We will use average formula to find test scores on 7th math quiz.

\text{Average of 7 math quizzes}=\frac{\text{Sum of scores on 7 math quizzes}}{\text{7 quizzes}}

77=\frac{x+450}{7}

Let us solve for x.

77\cdot 7=\frac{x+450}{7}\cdot 7

539=x+450

x+450=539

x+450-450=539-450

x=89

Therefore, Molly's score on the 7th math quiz was 89.

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LekaFEV [45]

Answer:

top right corner

Step-by-step explanation:

1) the green line

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thus, y ≤ x-2

3) the red line

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mars1129 [50]

Answer:

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Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

In this problem

If polygon RSUPE is similar to polygon KQUIC

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\frac{RS}{KQ}=\frac{RE}{KC}

substitutes the values and solve for a

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3 years ago
You are standing on a small fire tower 50 feet from a tree. You notice a squirrel in the tree. You measure the angle of depressi
irina [24]

Answer:

44.81 feet

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ACD

Find the length side AC (height of the small fire tower)

tan(52^o)=\frac{AC}{50} ---> by TOA (opposite side divided by the adjacent side)

Solve for AC

AC=tan(52^o){50}

AC=64\ ft

step 2

In the right triangle ABE

Find the length side AB

tan(21^o)=\frac{AB}{50} ---> by TOA (opposite side divided by the adjacent side)

solve for AB

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step 3

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Subtract the length side segment AB from the length side segment AC

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64-19.19=44.81\ ft

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