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
ladessa [460]
3 years ago
15

Find the work done by the force field F(x, y) = xi + (y + 6)j in moving an object along an arch of the cycloid r(t) = (t − sin(t

))i + (1 − cos(t))j, 0 ≤ t ≤ 2π.
Physics
1 answer:
Feliz [49]3 years ago
3 0

Answer:

177.65

Explanation:

Work done by the force field,F along path C is given by:

W=\int\limits_C F.dr

Given that:

r(t) = (t -sin(t)i + (1 -cos(t)j,\\\\\frac{dr}{dt}=(1-cos t)i+sin t\  j\\\\dr=(1-cos\  t)i +sin\  t \ j)dt\\\\F(x,y)=x\ i +(y+6)j\\\\F(r(t))=(t-sin \ t) i+((1-cos \t)+2)j\\\\\\

F(r(t))=(t-sin \ t)i+(3-cos \ t)j\\\\\\W=\int\limits_C F.dr\\=\int\limits^{6\pi}_0(t-sin \ t)i+(3-cos \ t)j).((1-cos \ t)i+sin \ t \ j)dt\\\\=\int\limits^{6\pi}_0(t-sin \ t)(1-cos \ t)+(3-cos \ t)sin \ t \ dt\\\\=\int\limits^{6\pi}_0t-tcos \ t+2sin\ t\ dt\\\\=\int\limits^{6\pi}_0-tcos \ t\ dt+[\frac{t^2}{2}-2cos \ t]\limits^{6\pi}_0\\\\=-I+177.65

#Integrating I by parts:

I=\int\limits^{6\pi}_0 tcos \ t \ dt\\\\=[\int \ tcos \ t \ dt]\limits^{6\pi}_0\\\\=[t\int cos \ t \ dt-\int (\frac{dt}{dt}\intcos \ t \ dt)dt]\limits^{6\pi}_0\\\\=[tsin\ t -\int sin\ t \ dt]\limits^{6\pi}_0\\\\=0

W=0+177.65

Hence, work done is 177.65

You might be interested in
If an object has a mass of 10 kilograms, how much does it weigh in newtons?
schepotkina [342]

10 kilograms of mass weighs 98.1 newtons on Earth,
16.2 newtons on the Moon, 37.1 newtons on Mars,
and other weights in other places.

6 0
3 years ago
The blood pressure in the human body is greater at the feet than at the brain
GarryVolchara [31]
Blood pressure is greater in feet because of gravity
5 0
3 years ago
Read 2 more answers
Will mark as brainliest if correct!!!!!!!!
ArbitrLikvidat [17]

Answer:

Light refracts when its speed changes as it enters a new medium.

Explanation:

Bending of light wave while it entering a medium with different speed is called refraction of light. Light passing from a faster medium to the slower medium bends the light rays toward the normal to boundary between two media. The amount of the  bending of light depends on refractive index of the two media which is described by  the Snell's Law. The angle of incidence is not equal to  angle of refraction. Rainbow is caused but this refraction phenomena. Also Refraction is used in magnifying glasses, prism and lenses

 

7 0
3 years ago
2. How long must a 400 W electrical engine work in order to produce 300 kJ of work?
yanalaym [24]

Answer:

Explanation:

400 W = 400 J/s

300000 J / 400 J/s = 750 s or 12.5 minutes

7 0
3 years ago
Help with science for A P E X
eimsori [14]

Answer:

inertia

Explanation:

7 0
3 years ago
Other questions:
  • I need an answer asap
    11·1 answer
  • Describe Ohm's law and its limitations;
    14·1 answer
  • What is the difference between a distance time graph and a speed time graph?
    9·1 answer
  • Inthisexperiment,aspringforcewasusedtokeep moving object travelingin a circularpath.The size of a spring force should be proport
    8·1 answer
  • The absolute magnitude of a star is the amount of light received by Earth. true or false
    14·2 answers
  • 60 point!!!
    14·1 answer
  • ASAP I’m timed on this so help would really be appreciated :)
    9·1 answer
  • A women weighs 857 N. What is her mass?
    13·2 answers
  • WhT is marasmus my followers and following pls give answer in detail ​
    12·2 answers
  • What happens when a magnet passes through a closed loop of wire?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!