A block of mass m is hung from the ceiling by the system of massless springs consisting of two layers. The upper layer consists of 3 strings in paralle, and the lower layer consists of 2 strings in parallel. The horizontal bar between the two layers has negligible mass. The force constants of all springs are k. Calculate the period of the vertical oscillations of the block.

Answers

Answer 1

Answer:

  T₀ = 2π [tex]\sqrt{\frac{m}{k} }[/tex]           T = [tex]\sqrt{\frac{5}{6} }[/tex] T₀

Explanation:

When the block is oscillating it forms a simple harmonic motion, which in the case of a spring and a mass has an angular velocity

        w = [tex]\sqrt{k/m}[/tex]

To apply this formula to our case, let's look for the equivalent constant of the springs.

Let's start with the springs in parallels.

* the three springs in the upper part, when stretched, lengthen the same distance, therefore the total force is

       F_total = F₁ + F₂ + F₃

the springs fulfill Hooke's law and indicate that the spring constant is the same for all three,

       F_total = - k x - k x - kx = -3k x

         

therefore the equivalent constant for the combination of the springs at the top is

      k₁ = 3 k

* the two springs at the bottom

following the same reasoning the force at the bottom is

        F_total2 = - 2 k x

the equivalent constant at the bottom is

         k₂ = 2 k

now let's work the two springs are equivalent that are in series

the top spring is stretched by an amount x₁ and the bottom spring is stretched x₂

            x₂ = x -x₁

            x₂ + x₁ = x

if we consider that the springs have no masses we can use Hooke's law

            [tex]-\frac{F_{1} }{k_{1} } - \frac{F_{2}}{k_{2} } = \frac{F}{k_{eq} }[/tex]

therefore the equivalent constant is the series combination is

             [tex]\frac{1}{k_{eq} } = \frac{1}{k_{1} } + \frac{1}{k_{2} }[/tex]

we substitute the values

             \frac{1}{k_{eq} }  = \frac{1}{3k } + \frac{1}{2k }  

             \frac{1}{k_{eq} }  = \frac{5}{6k} }  

              k_eq = [tex]\frac{6k}{5}[/tex]  

therefore the angular velocity is

             w = [tex]\sqrt{\frac{6k}{5m} }[/tex]  

           

angular velocity, frequency, and period are related

           w = 2π f = 2π / T

           T = 2π / w

            T = 2π [tex]\sqrt{\frac{5m}{6k} }[/tex]

           T₀ = 2π [tex]\sqrt{\frac{m}{k} }[/tex]

           T = [tex]\sqrt{\frac{5}{6} }[/tex] T₀


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Answer:

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Answers

Answer:

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Explanation:

We must remember that momentum is defined as the product of force by the time of force duration.

[tex]P=F*t[/tex]

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P = momentum [kg*m/s]

F = force [N]

t = time [s]

[tex]P=345*1.5\\P=517.5[kg*m/s][/tex]

explain why ionizing radiation is dangerous?​

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Answer:

When the dose is high enough, ionizing radiation causes two types of harm to humans: direct tissue damage and cancer. Direct tissue damage happens when enough molecules are broken apart that the cells simply can no longer function. This can lead to radiation burns, radiation sickness, organ failure, and even death.



A person lifts a heavy load to a vertical height of 2.0 m in 3 seconds. If he/she had done this more slowly in 6 seconds, the

work on the load would have been:

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half as great

the same

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Answers

Answer:

If the heavy load had been lifted more slowly, the work done on the load would have been the same.

Explanation:

Work done on an object is given as;

W = Fd

where;

F is the force applied on the object

d is the displacement of the object

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Also, the displacement of the object = vertical height the load was lifted.

W = mgh

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Thus, if the heavy load had been lifted more slowly, the work done on the load would have been the same.

A person lifting a heavy load to a vertical height of 2.0 m in 3 seconds does the same work as if he/she lifts it in 6 s.

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2 benefits of yoga with explanation

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14. After finishing her homework, Sue climbs up a 5.00 m high flight of stairs to her bedroom
Find the magnitude of Sue's weight
and how much
work Sue does in climbing the stairs if she
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Answers

Explanation:

Given parameters:

Height  = 5m

Mass of Sue  = 50kg

Unknown:

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Work done by Sue = ?

Solution:

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Mathematically;

        W = mg

m is the mass

g is the acceleration due to gravity  = 9.8m/s²

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Answers

Answer:

4770 N

Explanation:

Momentum is the product of mass and velocity and force is the change in momentum divided by change in time.

Given from the question;

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Answers

Answer:

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Answers

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Answer:

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Answers

Answer:

C

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Answers

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Answers

The following that are not true are E and D
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A 0.41kg football that is initially at rest acquires a velocity of 35m/s when it is kicked. If the kicker's boot remains in contact with the ball for 0.08s, what is the average force of the kick?

Answers

Answer:

F = 318.88[N]

Explanation:

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Answer:

98.0665 newtons

have a good day :]

a suspension bridge cable is connected to its anchor at a 20 degree angle. calculate the vertical component force on the anchor by the cable. ​

Answers

The question is missing some parts. Here is the complete question.

A suspension bridge cable is connected to its anchor at a 20° angle. Find the vertical and horizontal component of the force on the anchor by the cable.

Answer: [tex]F_{x}=[/tex] 14095.4 N

              [tex]F_{y}=[/tex] 5130.3 N

Explanation: The force applied to the anchor is not perpendicular to the horizontal plane. So, it can be decomposed into 2 components: a vertical component, which is on the y-axis, and a horizontal component, which is on the x-axis.

The force and its components forms a right triangle, so we can calculate the components by using trigonometric relations:

Horizontal

[tex]cos(20)=\frac{F_{x}}{F}[/tex]

[tex]F_{x}=F.cos(20)[/tex]

[tex]F_{x}=15,000(0.9397)[/tex]

[tex]F_{x}=[/tex] 14,095.4 N

Vertical

[tex]sin(20)=\frac{F_{y}}{F}[/tex]

[tex]F_{y}=Fsin(20)[/tex]

[tex]F_{y}=[/tex] 15,000(0.3420)

[tex]F_{y}=[/tex] 5,130.3 N

The vertical and horizontal components of force on the anchor by the cable are 5130.3 N and 14095.4 N, respectively.

fill in the blank:

the more people (greater mass) you load into a car, the ___ (more or less) it will accelerate with the same force applied by the engine.

Answers

the more people (greater mass) you load into a car, the more it will accelerate with the same force applied by the engine.

An inductor with an inductance of .5 henrys (H) is to be connected to a 60 Hz circuit. What will the inductive reactance (X L) be

Answers

Answer:

1885.2 ohms

Explanation:

Step one:

given data

L=5H

f=60Hz

Required

The inductive reactance of the inductor

Step two:

Applying the expression

XL= 2πfL

substitute

XL=2*3.142*60*5

XL=1885.2 ohms

Select all the correct answers.
Bella is writing a research paper on ocean currents. Which two sources should she consult?
an article published by a university or a government agency
an article from a website containing advertisements
an article published in 2015 and updated a week ago
an article appearing in the blog post of a teenage surfer
an article that does not state the author’s name and details

Answers

Answer: I belive the answer is

an article published by a university or a government agency and an article published in 2015 and updated a week ago

Ben runs from a position 3 m west of Main Street to a new position 45 m
west of Main Street in 6 seconds. What is Ben's velocity?
O
A. 7 m/s east
B. 7 m/s west
C. 8 m/s west
O
O
D. 8 m/s east
SUBMIT

Answers

Answer:

Option B. 7 m/s West.

Explanation:

From the question given above, the following data were obtained:

Position 1 (P₁) = 3 m West

Position 2 (P₂) = 45 m West

Time (t) = 6 s

Velocity (v) =?

Next, we shall determine the displacement of Ben. This can be obtained as follow:

Position 1 (P₁) = 3 m West

Position 2 (P₂) = 45 m West

Displacement =?

Displacement = P₂ – P₁

Displacement = 45 – 3

Displacement = 42 m West

Finally, we shall determine the velocity of Ben. This can be obtained as follow:

Time (t) = 6 s

Displacement (d) = 42 m West

Velocity (v) =?

v = d/t

v = 42 m West / 6 s

v = 7 m/s West

Thus the velocity of Ben is 7 m/s West

Will give brainliest if correct
Please help

Answers

Answer:

85.45

Divide 4,700/55

So C.

Answer:

C.85

Explanation:

Use the equation:

v= fλ ( v=wave speed, f= frequency, λ= wavelength)

4700= 55×λ

λ=4700÷55 =85.45 =85(approximately)

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