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Ira Lisetskai [31]

4 years ago

15

To practice Tactics Box 14.1 Identifying and analyzing simple harmonic motion. A complete description of simple harmonic motion

must take into account several physical quantities and various mathematical relations among them. This Tactics Box summarizes the essential information needed to solve oscillation problems of this type. The position of a 60 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. Determine the velocity at t=0.40s. Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be? What is the total energy E of the mass described in the previous parts?

1 answer:

bulgar [2K]4 years ago

7 0

Answer:

1.2x10^-3J

Explanation:

See attached file

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2000, the Millennium Bridge, a new footbridge over the River Thames in London, England, was opened to the public. However, after

sweet [91]

Answer:

n = 1810

A = 25 mm

Explanation:

Given:

Lateral force amplitude, F = 25 N

Frequency, f = 1 Hz

mass of the bridge, m = 2000 kg/m

Span, L = 144 m

Amplitude of the oscillation, A = 75 mm = 0.075 m

time, t = 6T

now,

Amplitude as a function of time is given as:

$A(t)=A_oe^{\frac{-bt}{2m}}$

or amplitude for unforce oscillation

$\frac{A_o}{e}=A_oe^{\frac{-b(6T)}{2m}}$

or

$\frac{6bt}{2m}=1$

or

$b=\frac{m}{3T}$

Now, provided in the question Amplitude of the driven oscillation

$A=\frac{F_{max}}{\sqrt{(k-m\omega_d^2)+(b\omega_d^2)}}$

the value of the maximum amplitude is obtained $(k=m\omega_d^2)$

thus,

$A=\frac{F_{max}}{(b\omega_d}$

Now, for n people on the bridge

Fmax = nF

thus,

max amplitude

$0.075=\frac{nF}{((\frac{m}{3T})2\pi}$

or

n = 1810

hence, there were 1810 people on the bridge

b) $A=\frac{F_{max}}{(b\omega_d}$

since the effect of damping in the millenium bridge is 3 times

thus,

b=3b

therefore,

$A=\frac{F_{max}}{(3b\omega_d}$

or

$A=\frac{1}{(3}A_o$

or

$A=\frac{1}{(3}0.075$

or

A = 0.025 m = 25 mm

6 0

3 years ago

For the material in the previous question that yields at 200 MPa, what is the maximum mass, in kg, that a cylindrical bar with d

Sedaia [141]

Answer:

The maximum mass the bar can support without yielding = 32408.26 kg

Explanation:

Yield stress of the material ( $\sigma$ ) = 200 M Pa

Diameter of the bar = 4.5 cm = 45 mm

We know that yield stress of the bar is given by the formula

Yield Stress = $\frac{Maximum load}{Area of the bar}$

⇒ $\sigma$ = $\frac{P_{max} }{A}$ ---------------- (1)

⇒ Area of the bar (A) = $\frac{\pi}{4}$ × $D^{2}$

⇒ A = $\frac{\pi}{4}$ × $45^{2}$

⇒ A = 1589.625 $mm^{2}$

Put all the values in equation (1) we get

⇒ $P_{max}$ = 200 × 1589.625

⇒ $P_{max}$ = 317925 N

In this bar the $P_{max}$ is equal to the weight of the bar.

⇒ $P_{max}$ = $M_{max}$ × g

Where $M_{max}$ is the maximum mass the bar can support.

⇒ $M_{max}$ = $\frac{P_{max} }{g}$

Put all the values in the above formula we get

⇒ $M_{max}$ = $\frac{317925}{9.81}$

⇒ $M_{max}$ = 32408.26 Kg

There fore the maximum mass the bar can support without yielding = 32408.26 kg

3 0

4 years ago

Answer in detail? Describe an activity that gives an understanding of ‘Electrostatic force’.

kvv77 [185]

Answer:

The electrostatic force is the force that exists between electrically charged particles or objects at rest.

8 0

3 years ago

The speed of a light wave in a certain transparent material is 0.6310.631 times its speed in vacuum, which is 3.00×108 m/s3.00×1

klemol [59]

Answer:

367.57 nm

Explanation:

Given that the speed of the light in certain material is 0.6310 times the speed of light in vacuum.

Speed of light in vacuum = 3×10⁸ m/s

Speed of the light in that material = 0.6310×3×10⁸ m/s = 1.893×10⁸ m/s

The frequency of the light does not change but the wavelength of the light changes with change in the speed when light travels from one medium to another.

Thus, frequency = 5.15×10¹⁴ Hz

Using,

c = frequency × Wavelength

Wavelength = c / frequency = (1.893×10⁸ m/s) / (5.15×10¹⁴ Hz) = 367.57×10⁻⁹ m

Also,

1 nm = 10⁻⁹ m

<u>So, wavelength = 367.57 nm</u>

5 0

3 years ago

Who is Janna Levin:

viva [34]

Answer:

Janna levin is a cosmologist and professor at physics.

She is an american by race

She was the presenter of Nova feature Black hole Apocalypse and has writtenany science non-fiction books

www.jannalevin.com is her own page where u get her correct info and bio

8 0

4 years ago