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
Brittany is saving up to purchase a new Xbox One S ANSWER FOR BRANLIEST Two Controller Bundle (1TB). She has already saved $425
Aleks [24]

Answer:

She will have to mow 7 lawns

Step-by-step explanation:

You do 425 -625 too see how much more money she needs

you get 175 . then each lawn is 25 so 175 divided by 25 is 7 . so she has mow 7 lawns

4 0
3 years ago
in a party,there is 40 percent more males than females.there are 475 males and females altogether.how many males were at the par
Phantasy [73]

The ratio of males to females is 1.4 : 1, so the fraction of the total that is made up of males is 1.4/(1.4 + 1) = 1.4/2.4 = 7/12.


There were (7/12)*475 ≈ 277 males at the party.

There were 475 - 277 = 198 females at the party.

7 0
3 years ago
What’s the answer to this???
AlexFokin [52]

Answer:

A i think

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The sum of 3 consecutive numbers is 27 what is the smallest number?
grandymaker [24]

Answer:

8

Step-by-step explanation:

8 plus 9 plus 10 equals 27. so 8 is the smallest.

4 0
3 years ago
Read 2 more answers
The first two terms of the perfect square trinomial are given, find "c".
Naddik [55]

Answer:

A.) 36

Step-by-step explanation:

For a perfect square trinomial, a = 1  b = 2x  c = x².  For an example, (x+3)² = x² + 6x + 9.

For this trinomial, divide "b" by 2 to get 6.  Square this number and you will have 36.

x² + 12x + 36

7 0
3 years ago
Read 2 more answers
Other questions:
  • You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Write an expression which describes the per
    6·2 answers
  • Which of the following is the multiplicative inverse of 2x?<br> 1/2 X<br> -1/2 X<br> -2x<br> 2x
    15·1 answer
  • Antoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00. Tess says, “It is easy to find 10% of 46 by m
    10·1 answer
  • Let ABC be a right triangle with legs AB = 8 cm and AC = 9 cm. What is the largest possible area of a rectangle ADEF if the poin
    6·1 answer
  • What is the value of H?
    15·1 answer
  • The domain of the function given below is the set of all real numbers true or false; f(x)=(1/2)^x
    13·2 answers
  • Please help with this
    6·1 answer
  • F(x)=-3x • G(x) = x +7
    6·1 answer
  • Consider the formula for the average velocity, v, of a moving particle. In the formula, d1 and d2 represent the distance travele
    5·1 answer
  • 1. Which is the better deal?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!