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
scZoUnD [109]
3 years ago
12

A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re

quired to stretch it from 7 m to 13 m?
Mathematics
1 answer:
bezimeni [28]3 years ago
5 0

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force F and the distance d  that the object moves:

W=Fd

If F is measured in newtons and d<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

W=\int\limits^b_a {f(x)} \, dx

Hooke’s Law states that the force required to maintain a spring stretched x    units beyond its natural length is proportional to

f(x)=kx

where k is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1

Thus F=x

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18

18 J is the work required to stretch a spring from 7 m to 13 m.

You might be interested in
What is equal to 14.1.
VLD [36.1K]
A lot of numbers, equations, etc equal 14.1. Be more specific in your questions. I’m sorry this doesn’t really help but just use this for future reference
3 0
3 years ago
Please help asap will give brainliest if correct.
professor190 [17]

Answer:

x¹²,8x⁴,6x,2x,1

Step-by-step explanation:

x²×x⁶×x⁴=x¹²

x^4(8) =8x⁴

x^1(6) =6x

x^1(2) =2x

x^0 = 1

3 0
3 years ago
A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 and $0.85 per mile. What inequality repre
spin [16.1K]

Answer:

.

Step-by-step explanation:

0.85x + 375 > 450

5 0
3 years ago
The seventh grade class is putting on a verity shell to raise money it cost 1700 to rent the banquet hall That they are going to
MaRussiya [10]

Answer:

g

Step-by-step explanation:

3 0
3 years ago
If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq<br><br>​
Butoxors [25]

By way of example, suppose <em>A</em> = {1, 2, 3} and <em>B</em> = {<em>a</em>, <em>b</em>, <em>c</em>}. Then the Cartesian product of <em>A</em> and <em>B</em> is

<em>A</em> × <em>B</em> = {{1, <em>a</em>}, {1, <em>b</em>}, {1, <em>c</em>}, {2, <em>a</em>}, {2, <em>b</em>}, {2, <em>c</em>}, {3, <em>a</em>}, {3, <em>b</em>}, {3, <em>c</em>}}

That is, each element in <em>A</em> gets a pairing with each element in <em>B</em>, and for each pairing you have <em>n(A)</em> choices for the first element and <em>n(B)</em> choices for the second element.

So if <em>n(A)</em> = <em>p</em> and <em>n(B)</em> = <em>q</em>, then <em>n(A</em> × <em>B)</em> = <em>pq</em>.

6 0
3 years ago
Other questions:
  • Suppose a triangle reflects over the y-axis. Which describes how the transformation affects the coordinates of the vertices?
    8·2 answers
  • Can the square root of 130 be simplified.
    14·2 answers
  • The probability of an event A occurring is 0.73. Determine . P(A) a)0.73 b)0.00 c)0.27 d)1.00
    10·2 answers
  • PLEASE HELP ME ASAP!!! The diagonal of Andres rectangular TV screen is 39 in. The width of his TV screen is 34 inches. which mea
    10·1 answer
  • Write 0.0000000001 in scientific notation
    7·2 answers
  • Kim wants to draw a triangle with a 20 degrees angle and a 70 degrees angle so that the side between them is 4 inches long. How
    6·1 answer
  • A rectangle with a perimeter of 19m^2+2m-10 and a width of m^2 write an expression for the lenght
    9·1 answer
  • Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls-going on t
    12·1 answer
  • ⚠️❗️⚠️❗️⚠️❗️ 100 POINTS TO ANSWER ALL FOUR QUESTIONS IF YOU PUT A TROLL ANSWER OR A LINK I SWEAR TO GOD I’LL REPORT YOU ON 3 ALT
    9·2 answers
  • Divide £88 between Bill and Sam. If Sam gets
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!