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
Yakvenalex [24]
2 years ago
13

A 60 kg acrobat is in the middle of a 10 m long tightrope. The center of the rope dropped 30 cm in relation to the ends that are

attached to fixed supports. What is the tension in each half of the rope?
Physics
1 answer:
Zigmanuir [339]2 years ago
4 0

Answer:

The tension in each half of the rope, is approximately 4,908.8 N

Explanation:

The mass of the acrobat, m = 60 kg

The length of the rope, l = 10 m

The extent by which the center dropped = 30 cm = 0.3 m

Let, 'T' represent the tension in each half of the rope

Weight, W = Mass, m × The acceleration due to gravity, g

∴ W = m × g

The acceleration due to gravity, g ≈ 9.8 m/s²

∴ The weight of the acrobat, W = 60 kg × 9.8 m/s² ≈ 588 N

The angle the dropped rope makes with the horizontal, θ is given as follows;

θ = arctan((0.3 m)/(5 m)) = arctan(0.06) ≈ 3.434°

At equilibrium, the sum of vertical forces, \Sigma F_y = 0

The vertical component of the tension, T_y, in each half of the rope is given as follows;

T_y = T × sin(θ)

∴ \Sigma F_y = W + T × sin(θ) + T × sin(θ) = W + 2 × T × sin(θ)

Plugging in the values, with θ = arctan(0.06) for accuracy, we get;

588 N + 2 × T × sin(arctan(0.06) = 0

∴ 2 × -T × sin(arctan(0.06) = 588 N

-T= 588 N/(2 × sin(arctan(0.06)) = 4,908.81208 N ≈ 4,908.8 N

The tension in each half of the rope, T ≈ 4,908.8 N.

You might be interested in
The movement of a magnetic pole away from the actual pole
Lunna [17]

The North Magnetic Pole is the point on the surface of Earth's Northern Hemisphere at which the planet's magnetic field points vertically downwards (in other words, if a magnetic compass needle is allowed to rotate about a horizontal axis, it will point straight down). There is only one location where this occurs, near (but distinct from) the Geographic North Pole and the Geomagnetic North Pole.
3 0
3 years ago
A ball is projected upward at time t=0.0s, from a point on a roof 90m above the ground. The ball rises, then falls and strikes t
chubhunter [2.5K]
As v becomes zero at the highest point, i prefer considering different travelling directions so it will become less complicated.
dont forget to add the total time up .

also to master the skills, write down the "uvsat" may help (thats the way i found it easier to handle problems)

4 0
3 years ago
Acid mine drainage is:
Dahasolnce [82]

Answer:

Acid mine drainage is dissolved toxic materials wash from mines into nearby lakes and streams.

Explanation:

Acid mine drainage is the flow of acidic water with pH typically between 2 and 4, and high concentrations of other dissolved toxic materials from mines into nearby lakes and streams. It mainly occurs during metal sulfide mining, when the metal sulfide ore such as pyrite (FeS2) is exposed to water and oxygen from air to produce soluble iron and sulfuric acid.

Microorganisms, especially acidophile bacteria like Acidithiobacillus ferrooxidans grow by pyrite oxidation, i.e., oxidizing the Fe²⁺ in pyrite to Fe³⁺, which again react with pyrite and water to produce sulfuric acid. Then the acidic water flows into nearby water sources and reduces the pH value of water in those sources. As a result, heavy metals such as copper, lead, mercury, etc in other mineral ores also get dissolved into the water. The action of acidophile bacteria also increases the rate and degree of acid-mine drainage process.

The acid mine drainage causes water pollution and adversely affect the aquatic plants and animals. It also results in the contamination of drinking water, corrosion of infrastructures such as bridges, etc.

8 0
3 years ago
What is/are the difference between wavelength and spectral lines?
Gre4nikov [31]

Answer:

<u><em>Definition of spectral line: </em></u><em>one of a series of linear images formed by a spectrograph or similar instrument and corresponding to a narrow portion of the spectrum of the radiation emitted or absorbed by a particular source.</em>

<em />

<u><em>Definition of Wavelength:</em></u><em> can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave. ... Wavelength is inversely proportional to frequency. This means the longer the wavelength, lower the frequency.</em>

<em />

<em>So, the spectrum is the range of wavelength in visible light. While, wavelength is the length of a wave.</em>

<em></em>

Explanation:

I hope this helps!

8 0
2 years ago
A vector has an x-component
9966 [12]

Explanation:

The magnitude of a vector v can be found using Pythagorean's theorem.

||v|| = √(vₓ² + vᵧ²)

||v|| = √((-309)² + (187)²)

||v|| ≈ 361

You can find the angle of a vector using trigonometry.

tan θ = vᵧ / vₓ

tan θ = 187 / -309

θ ≈ 149° or θ ≈ 329°

vₓ is negative and vᵧ is positive, so θ must be in the second quadrant.  Therefore, θ ≈ 149°.

4 0
3 years ago
Other questions:
  • A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250 s. The total energy
    13·1 answer
  • What is the electric power used by an appliance if the current is 2 A and the voltage is 50 volts? Show work and include all uni
    11·1 answer
  • How do inertia and centripetal force combine to keep an object moving in circular motion?
    13·2 answers
  • A liter is the same as a cubic meter. <br> a. True<br> b. False
    12·2 answers
  • As soon as parachute of a falling soldier opens, how will the accleration change?​
    9·1 answer
  • Find equivalent resistance between A and B​
    11·1 answer
  • A motor has a rotor (with armature) of moment of inertia ????m . The rotor is attached to a gear box of gear ratio G &gt; 1. The
    14·1 answer
  • PLEASE HELP!!!!I IM GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (30pts)
    14·1 answer
  • Help me pleaseeeeee due. Today
    6·2 answers
  • The equivalent resistance of a series combination of resistors is always greater than any individual resistance
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!