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
Ber [7]
3 years ago
9

A 40-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain

has a density of 10 kg/m. Use 9.8 m/s2 for the acceleration due to gravity.
a) How much work is required to wind the entire chain onto the cylinder using the winch?
b) How much work is requeired to wind the chain onto the cylinder if a 25-kg block is attached to the end of the chain??
a) The amount of work required is ____??? J. (Type an integer or a decimal)
b) The amount of work required is ____??? J. (Type an integer or a decimal)
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

a) W₁ = 78400 [J]

b)Wt = 82320 [J]  

Step-by-step explanation:

a) W = ∫ f*dl      general expression for work

If we have a chain with density of 10 Kg/m, distributed weight would be

9.8 m/s² * 10 kg   = mg

Total length of th chain is 40 m, and the function of y at any time is

f(y) = (40 - y ) mg   where ( 40 - y ) is te length of chain to be winded

At the beggining we have to wind 40 meters   y = 0 at the end of the proccess  y = 40 and there is nothing to wind then:

f(y) = mg* (40 - y )

W₁ =  ∫f(y) * dy    ⇒ W₁ = ∫₀⁴⁰ mg* (40 - y ) dy  ⇒ W₁ = mg [ ∫₀⁴⁰ 40dy - ∫₀⁴⁰ ydy

W₁ = mg [ 40*y |₀⁴⁰   -  1/2 * y²  |₀⁴⁰    ⇒  W₁ = mg* [ 40*40 - 1/2 (40)² ]

W₁ = mg * [1/2]     W₁ = 10*9,8* ( 800 )

W₁ = 78400 [J]

b) Now we can calculate work to do if we have a 25 block and the chain is weightless

W₂ = ∫ mg* dy     ⇒    W₂  = ∫₀⁴⁰ mg*dy   ⇒    W₂  = mg y |₀⁴⁰

W₂ = mg* 40   = 10*9.8* 40  

W₂ = 3920 [J]

Total work

Wt = W₁  +  W₂        ⇒    Wt = 78400 + 3920

Wt = 82320 [J]

You might be interested in
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3604 to rent
agasfer [191]

Answer: 14 tons

$3,860.50

Step-by-step explanation:

Let x = the amount of sugar transported.

First company:

The cost is $3157 truck rental plus $50.25 per ton of sugar.

Total cost = 3157 + 50.25x dollars

Second company:

There is no charge for truck rental, but it costs $275.75 per ton of sugar.

The total cost is

275.75x

When the two costs are the same, then

275.75x = 3157 +50.25x

225.5x = 3157

x = 14 tons

The total cost is 275.75*14 = $3,860.50

5 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLIEST
Alex

Answer:

c

Step-by-step explanation:

(3.14)(15*15)(315)=222548

5 0
3 years ago
What’s the solution of 2 plus 2
egoroff_w [7]

Answer: 4

Step-by-step explanation: 2 + 2 = 4

8 0
3 years ago
Read 2 more answers
PLS HELP MY GRADES CLOSE TOMMORW Which side lengths form a right triangle?
Anna35 [415]
Letter A is right


Explanation: best of luck
7 0
3 years ago
Read 2 more answers
Dexter had 15 fish in the fish tank. 7 were goldfish and the rest were neon tetra fish. Then he added 4 neon tetra fish. How man
Evgesh-ka [11]

Answer:

answer is 12

Step-by-step explanation:

if you take 15 and subtract it by 7 that would give you the number of neon tetra fish, then you can add 4 to give you your total number which is 12 :)

7 0
3 years ago
Other questions:
  • 9 apples there are 6 fewer apples than oranges
    6·1 answer
  • Siera has 11.5 yards of yarn. she uses a certain amount for a project, leaving 5.25 yards of yarn. The equation 11.5 - x = 5.25
    6·1 answer
  • In an alloy of copper and tin, there is 85% of copper. How much of this alloy do you need in order to get 1 13/32 lb of tin?
    5·1 answer
  • Given a normal distribution with mu equals 100μ=100 and sigma equals 10 commaσ=10, complete parts​ (a) through​ (d). loading...
    9·1 answer
  • Which name accurately describes the figure shown below?
    7·2 answers
  • I need serious Help!
    5·1 answer
  • These questions are from financial liteeracy
    13·1 answer
  • Geometry help please. Complete the similarity statement, in the box below, of these two triangles.
    6·1 answer
  • Suppose $500 is invested at 6% annual interest compounded twice a year. When will the investment be worth $1000.
    10·1 answer
  • What is the common ratio of this sequence: 4, 20, 100...?<br><br> pls
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!