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Salsk061 [2.6K]

3 years ago

7

Pin p is constrained to move along the curve defined by the lemniscate r=(4sin2θ)ft.if the slotted arm oa rotates counterclockwi

se with a constant angular velocity of θ˙ = 1.0 rad/s , determine the magnitude of the velocity of peg p when θ = 59 ∘.

1 answer:

ruslelena [56]3 years ago

5 0

position of the peg is given by the equation

$r = 4 sin2\theta$

now the rate of change in position is given as

$v = \frac{dr}{dt}$

$v = \frac{d}{dt}(4 sin2\theta)$

$v = 8cos2\theta*\frac{d\theta}{dt}$

$v = 8 cos2\theta*\omega$

given that

$\omega = 1 rad/s$

$\theta = 59 degree$

now we have

$v = 8*cos(2*59)* 1 = -3.76 m/s$

<em>so its speed will be 3.76 m/s in magnitude</em>

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To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.

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Here,

M = Mass

R = Radius of the hoop

The precession frequency is given as

$\Omega = \frac{Mgd}{I\omega}$

Here,

M = Mass

g= Acceleration due to gravity

d = Distance of center of mass from pivot

I = Moment of inertia

$\omega$ = Angular velocity

Replacing the value for moment of inertia

$\Omega= \frac{MgR}{MR^2 \omega}$

$\Omega = \frac{g}{R\omega}$

The value for our angular velocity is not in SI, then

$\omega = 1000rpm (\frac{2\pi rad}{1 rev})(\frac{1min}{60s})$

$\omega = 104.7rad/s$

Replacing our values we have that

$\Omega = \frac{9.8m/s^2}{(8*10^{-2}m)(104.7rad)}$

$\Omega = 1.17rad/s$

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$T = \frac{2\pi rad}{\Omega}$

$T = \frac{2\pi}{1.17}$

$T = 5.4 s$

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3 years ago

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What f

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Answer:

the force constant k = 2.369 N/m

Explanation:

Given that:

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair.

with period T = 0.500 s and a mass of 0.0150 kg, Then the force constant can be calculated by using the formula:

$\mathtt{T = 2 \pi \ \sqrt{\dfrac{m}{k} }}$

where;

T = time period

m = mass

k = force constant.

By making k the subject of the formula; we have:

$\mathtt{T^2 = 4 \pi^2 (\dfrac{m}{k})}$

$\mathtt{k =\dfrac{4 \pi ^2 \ m}{T^2}}$

replacing our given values , we have:

$\mathtt{k =\dfrac{4 (3.142) ^2 \ \times 0.0150 }{0.5^2}}$

$\mathtt{k =\dfrac{39.49 \ \times 0.0150 }{0.25}}$

$\mathtt{k =\dfrac{0.59235 }{0.25}}$

k = 2.369 N/m

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3 years ago

La intensidad de corriente que circula por un conductor es 2μA. ¿Que tiempo demoraran 5x1013 electrones en cruzar una determinad

VikaD [51]

Answer:

t = 4 seconds

Explanation:

The question is "The intensity of current flowing through a conductor is 2μA. How long will it take 5x1013 electrons to cross a certain cross section of the conductor? "

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No of electrons, $n=5\times 10^{13}$

We need to find how long will it take to given no of electrons to cross a certain cross section of the conductor.

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Also, q = ne

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3 years ago

A singly ionized helium atom is in the ground state. It absorbs energy and makes a transition to the n = 3 excited state. The io

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Answer:

$\lambda=25.6nm$

Explanation:

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$\frac{1}{\lambda}=RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

Where R is the Rydberg constant of the element, Z its atomic number, $n_1$ is the lower energy level and $n_2$ the upper energy level of the electron transition. Recall that the ground state is denoted as n=1.

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3 years ago

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Answer:

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Explanation:

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a = -9.8 m/s²

t₀ = 0 s

y = y₀ + v₀ t + ½ at²

y = 81.5 − 4.9t²

For the second object:

y₀ = 0 m

v₀ = 40.0 m/s

a = -9.8 m/s²

t₀ = 2.20 s

y = y₀ + v₀ t + ½ at²

y = 40(t−2.2) − 4.9(t−2.2)²

When they meet:

81.5 − 4.9t² = 40(t−2.2) − 4.9(t−2.2)²

81.5 − 4.9t² = 40t − 88 − 4.9 (t² − 4.4t + 4.84)

81.5 − 4.9t² = 40t − 88 − 4.9t² + 21.56t − 23.716

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y = 81.5 − 4.9(3.139)²

y = 33.2

7 0

3 years ago