A mineral's chemical composition and crystal structure help determine it's __________

An oscillator consists of a block attached to a spring (k = 427 N/m). At some time t, the position (measured from the system's e

White raven [17]

Answer:

a) 4.49Hz

b) 0.536kg

c) 2.57s

Explanation:

This problem can be solved by using the equation for he position and velocity of an object in a mass-string system:

$x=Acos(\omega t)\\\\v=-\omega Asin(\omega t)\\\\a=-\omega^2Acos(\omega t)$

for some time t you have:

x=0.134m

v=-12.1m/s

a=-107m/s^2

If you divide the first equation and the third equation, you can calculate w:

$\frac{x}{a}=\frac{Acos(\omega t)}{-\omega^2 Acos(\omega t)}\\\\\omega=\sqrt{-\frac{a}{x}}=\sqrt{-\frac{-107m/s^2}{0.134m}}=28.25\frac{rad}{s}$

with this value you can compute the frequency:

a)

$f=\frac{\omega}{2\pi}=\frac{28.25rad/s}{2\pi}=4.49Hz$

b)

the mass of the block is given by the formula:

$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}\\\\m=\frac{k}{4\pi^2f^2}=\frac{427N/m}{(4\pi^2)(4.49Hz)^2}=0.536kg$

c) to find the amplitude of the motion you need to know the time t. This can computed by dividing the equation for v with the equation for x and taking the arctan:

$\frac{v}{x}=-\omega tan(\omega t)\\\\t=\frac{1}{\omega}arctan(-\frac{v}{x\omega })=\frac{1}{28.25rad/s}arctan(-\frac{-12.1m/s}{(0.134m)(28.25rad/s)})=2.57s$

Finally, the amplitude is:

$x=Acos(\omega t)\\\\A=\frac{0.134m}{cos(28.25rad/s*2.57s )}=0.45m$

5 0

2 years ago

What is friction and explain

Veseljchak [2.6K]

Friction is the force you get when you (for example) Rub something with another, it's a force that may generate heat and even some resistance. Another example is rubbing your hands together, they get hot, therefore friction is working, without friction you wouldn't be able to stop moving.

8 0

2 years ago

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Select the correct answer. Which of the following causes air pollution inside the house? A. Smoking cigarettes B. Growing housep

Troyanec [42]

Answer: Smoking cigarettes

Explanation: The other options don't cause pollution to form in the air besides smoking, from the particles it creates causing harm and damage to your lungs and fill the air with smoke particles.

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2 years ago

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An engineer is designing a small toy car that will be launched from rest. The engineer wants to maximize the kinetic energy of t

aalyn [17]

The modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly (option B).

<h3>What is kinetic energy?</h3>

Kinetic energy is the energy possessed by an object because of its motion. The kinetic energy equal (nonrelativistically) to one half the mass of the body times the square of its speed.

According to this question, an engineer is designing a small toy car that will be launched from rest. The engineer wants to maximize the kinetic energy of the car when it is launched by a compressed spring.

However, he can only make one adjustment to the initial conditions of the car. Considering the fact that the mass of an object is directly proportional to the kinetic energy.

This suggests that the modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly.

Learn more about kinetic energy at: brainly.com/question/12669551

#SPJ1

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1 year ago

A circle is 360°. What percentage of a circle is 90°?

kykrilka [37]

Answer:

360 ÷ 4 = 90

Example

A 360° circle is cut into 4 peaces in the form of + or × . It's one side is called 90°

6 0

3 years ago

A mineral's chemical composition and crystal structure help determine it's ___________.