1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lubov Fominskaja [6]
3 years ago
15

Consider a semicircular ring of radius R. Its linear mass density varies as lambda =lambda not sin theta. Locate its centre of m

ass​

Physics
1 answer:
bearhunter [10]3 years ago
4 0

Answer:

(0, πR/4)

Explanation:

The linear mass density (mass per length) is λ = λ₀ sin θ.

A short segment of arc length is ds = R dθ.

The mass of this short length is:

dm = λ ds

dm = (λ₀ sin θ) (R dθ)

dm = R λ₀ sin θ dθ

The x coordinate of the center of mass is:

X = ∫ x dm / ∫ dm

X = ∫₀ᵖ (R cos θ) (R λ₀ sin θ dθ) / ∫₀ᵖ R λ₀ sin θ dθ

X = R ∫₀ᵖ sin θ cos θ dθ / ∫₀ᵖ sin θ dθ

X = R ∫₀ᵖ ½ sin 2θ dθ / ∫₀ᵖ sin θ dθ

X = ¼R ∫₀ᵖ 2 sin 2θ dθ / ∫₀ᵖ sin θ dθ

X = ¼R (-cos 2θ)|₀ᵖ / (-cos θ)|₀ᵖ

X = ¼R (-cos 2π − (-cos 0)) / (-cos π − (-cos 0))

X = ¼R (-1 + 1) / (1 + 1)

X = 0

The y coordinate of the center of mass is:

Y = ∫ y dm / ∫ dm

Y = ∫₀ᵖ (R sin θ) (R λ₀ sin θ dθ) / ∫₀ᵖ R λ₀ sin θ dθ

Y = R ∫₀ᵖ sin² θ dθ / ∫₀ᵖ sin θ dθ

Y = R ∫₀ᵖ ½ (1 − cos 2θ) dθ / ∫₀ᵖ sin θ dθ

Y = ½R ∫₀ᵖ (1 − cos 2θ) dθ / ∫₀ᵖ sin θ dθ

Y = ½R (θ − ½ sin 2θ)|₀ᵖ / (-cos θ)|₀ᵖ

Y = ½R [(π − ½ sin 2π) − (0 − ½ sin 0)] / (-cos π − (-cos 0))

Y = ½R (π − 0) / (1 + 1)

Y = ¼πR

You might be interested in
What is the definition of visible white light wave (RoyGBive)
uranmaximum [27]

There's no such thing as a wave of white light.  Every light wave with
a certain wavelength has some color.  White light is a mixture of all
the different wavelengths with all of the different visible colors. 
They're ALL there in white light.  When they all enter your eye at
the same time, your brain gets the message of brightness with
no particular color, which we call "white light".

5 0
3 years ago
A particular form of electromagnetic radiation has a frequency of 5.42x10^15 Hz. What is the wavelength is nanometers? meters?
zubka84 [21]
Electromagnetic radiation are represented in waves. Each type of wave has a certain shape and length. The distance between two peaks in a wave is called the wavelength. This value is equal to the speed of light divided by the frequency.
Wavelength = c/f
Wavelength = 3x10^8 / <span>5.42x10^15
</span><span>Wavelength = 5.54 x 10^-8 m = 55.35 nm</span>
4 0
3 years ago
Compared to Earth's moon, the moons of Mars are
Mice21 [21]
I think is b I think
7 0
2 years ago
A long. 1.0 kg rope hangs from a support that breaks, causing the rope to fall, if the pull exceeds 43 N. A student team has bui
raketka [301]

Answer:

6.8 m/s2

Explanation:

Let g = 9.8 m/s2. The total weight of both the rope and the mouse-robot is

W = Mg + mg = 1*9.8 + 2*9.8 = 29.4 N

For the rope to fails, the robot must act a force on the rope with an additional magnitude of 43 - 29.4 = 13.6 N. This force is generated by the robot itself when it's pulling itself up at an acceleration of

a = F/m = 13.6 / 2 = 6.8 m/s2

So the minimum magnitude of the acceleration would be 6.8 m/s2 for the rope to fail

8 0
3 years ago
Which of the following is not a petroleum product
serg [7]
D. wool     
hope it helped
4 0
3 years ago
Other questions:
  • The capacitor can withstand a peak voltage of 590 volts. If the voltage source operates at the resonance frequency, what maximum
    13·1 answer
  • How is lightning formed with explanation l?
    7·1 answer
  • In the equilibrium position, the 30-kg cylinder causes a static defl ection of 50 mm in the coiled spring. If the cylinder is de
    6·1 answer
  • What important discovery was made by edmond halley and alexis clairaut, using newton's ideas of mathematics and gravity?
    5·2 answers
  • ASAP ONLY ACTUAL CORRECT ANSWERS
    11·2 answers
  • You wish to lift a 12,000 lb stone by a vertical distance of 15 ft. Unfortunately, you can only generate a maximum pushing force
    5·1 answer
  • The more POWER you use to move an object, the more work you do.
    9·2 answers
  • 3. Why is the term cold blooded a misconception? Explain​
    8·1 answer
  • Pls help me with this one :)) ​
    11·1 answer
  • F each fission reaction in a nuclear reactor emits three neutrons, how many neutrons are produced from three fission reactions?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!