Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 30 centimeters to 60 centimeters?

Answers

Answer 1

Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

[tex]F =450N[/tex]

[tex]x_1 = 30cm[/tex]

[tex]x_2 = 60cm[/tex]

Required

The work done

First, we calculate the spring constant (k)

[tex]F = kx_1[/tex]

[tex]450N = k *30cm[/tex]

[tex]k = \frac{450N}{30cm}[/tex]

[tex]k =15N/cm[/tex]

So:

[tex]F = kx_1[/tex]

[tex]F(x) = 15x[/tex]

The work done using Hooke's law is:

[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]

This gives:

[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]

Rewrite as:

[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]

Integrate

[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]

This gives:

[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]

[tex]W =15 *\frac{2700}{2}[/tex]

[tex]W =15 *1350[/tex]

[tex]W =20250N-cm[/tex]

Convert to Nm

[tex]W =\frac{20250Nm}{100}[/tex]

[tex]W =202.50Nm[/tex]


Related Questions

Now that we know that 2π is about 6.28, π2 is about 9.86, and 58−−√ is between 7 and 8, which choice represents the correct order of these expressions from least to greatest: 58−−√, 2π, π2, 8?

Answers

Answer:

use miss r sir hope I helped you

Need help ASAP NO LINKS

Answers

Answer:

9

Step-by-step explanation:

5(n-2)=35

5n-10=35

5n=35+10

5n=45

n=45/5

n=9

Please mark me as brainliest

hope this helps! feel free to clarify

1. What is the discriminant of the equation 5x2 - 20x + 20 = 0?

Answers

Answer:

0

Step-by-step explanation:

D = 20²-4(5)(20) = 400-400 = 0

What is the quotient when (-12x9 + 3x7 + 24x6) is divided by 6x?

Answers

-2x^8+.5x^6+4x^5 is the quotient.

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12) = 4.00. If the researcher had used an ANOVA to evaluate the data, what F-ratio would be obtained?

a. F(1, 11) = 2.00
b. F(1, 12) = 16.00
c. F(1, 12) = 2.00
d. F(1, 11) = 16.00

Answers

Answer:

B). F(1, 12) = 16.00

Step-by-step explanation:

'ANOVA' is a measure employed for 'analysis of a variance' in a given set of data of treatments or populations. While t-test helps in comparing their means.

As per the question, the F-ratio using ANOVA would be 'F(1, 12) = 16.00.' In order to calculate the variances, the distinction among the samples. The б^2 denotes the difference of representative means which is augmented by n(in case of samples being same). So, the ratio of F(1, 12) would be б^2 i.e. 4^2 = 16 since the sample sizes are distinct. Thus, option B is the correct answer.

I need help with this algebra question

Answers

Answer:

4.58258

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

Input:

2² + x² = 5²

Remember, c² is always the side opposite of the right angle...

4 + x² = 25

21 = x²

x = 4.58258

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

[tex]\sqrt{21}[/tex]

Step-by-step explanation:

let the missing side be x , then

Using Pythagoras' identity in the right triangle.

x² + 2² = 5²

x² + 4 = 25 ( subtract 4 from both sides )

x² = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex] ≈ 4.6 ( to 1 dec. place )

Consider the division of 8y2 – 12y + 4 by 4y.





What are the values of a and b?

Answers

Answer:

Step-by-step explanation:

8y^2 -12y +4 / 4y = 2y -3     so from this result that a=2y and b= - 3

8y^2

The radius of a circle is 9in. Find it’s circumference in terms of

Answers

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 9 in.

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The circumference of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]

[tex] = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in[/tex]

Therefore, the circumference of the circle is 56.52 in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Help again pleaseeeee

Answers

It’s D
Hope it helps :)

Lisa played two rounds of
miniature golf. Her score was –3 in the
first round and +2 in the second round.
What was Lisa's score after two
rounds?

Answers

Answer:

-1 I think so.....

n please rate this

Lisa’s score after two rounds is -1
Explanation:
1st round: -3
2nd round: 2
-3 + 2 = -1

I really hope this helps!
Glad to help, I also want to know if my answer was right.

Favorite Sport Use the table to identify the labels for the segmented bar graph. Favorite Sport Male Female Football 10 2 Relative Frequency 100 90 80 70 60 50 40 30 20 OB OA Soccer 8 9 Basketball 7 6 Label A is 10 Label B is 0 Label C is < С C D E Label D is Sport Label E is < Intro Done​

Answers

The labels for the segmented bar graph include:

Label A is MaleLabel B Is FemaleLabel C is FootballLabel D Is SoccerLabel E Is Basketball

What is a bar graph?

A bar graph is a graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.

Here, the identification of the labels for the segmented bar graph has been depicted based on the information.

Learn more about bar graph on:

https://brainly.com/question/24741444

#SPJ1

What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25

Answers

Answer:

the answer is a.12

i think

Answer:

17.25

Step-by-step explanation:

What is the greatest prime you must consider to test whether 4295 is​ prime?

Answers

Answer:

5

Step-by-step explanation:

4295/5 = 859

4295 is divisible by the prime number 5

no need to test any higher priime

between which two consecutive numbers does the square root of 90 lie

Answers

Answer:

It lies between the number 9 and 10.

Step-by-step explanation:

Your Welcome, hope this helps:)

Answer:

We all know that every square root lies between the square root of two perfect squares. Hence, √90 lies between the consecutive numbers 9 and 10.

Step-by-step explanation:

k

3. (a) Find the elasticity of the demand function p2 + 2p +
4 = 49 at p = 6.

(b) How will a price increase affect total revenue?​

Answers

Answer:

6^2+12+4=49

36+16=49

52=49

therefore.3

Let's start! Take a look at all of these blocks. You can reach the number 10 by adding the blocks in many different ways. BUT, what is the LEAST number of blocks you need to add together in order to reach the number 10?

Answers

Answer:

the answer is 2. (6 and 4)

Step-by-step explanation:

6 + 4 = 10

Question is on the screenshot

Answers

Answer:

Volume of cylinder = 192π inch³

Step-by-step explanation:

Given:

Diameter of base = 8 inch

Length of cylinder = 12 inch

Find:

Volume of cylinder

Computation:

Radius of cylinder = Diameter of base / 2

Radius of cylinder = 8 / 2

Radius of cylinder = 4 inch

Volume of cylinder = πr²h

Volume of cylinder = π(4)²(12)

Volume of cylinder = π(16)(12)

Volume of cylinder = 192π inch³

Find the area

76 sq meters
60 sq meters
30.5 sq meters
65 sq meters

Answers

Step-by-step explanation:

2*10+((4+10)x8)/2

=20+14*8/2

=76 sq meters

The measure of _A is 18° greater than the measure of _B. The two angles are complementary. Find the
measure of each angle.
The m_A is
1° m
and m_B is

Answers

Answer:

angle A=54 degree

angle B =36 degree

Step-by-step explanation:

let angle B be x

angle A=x+18

since they are complementary angles sum of these two angles will be 90 degree

x+x+18=90

2x=90-18

2x=72

x=72/2

x=36 degree

substitute the value of x to find angle A and angle B

for angle A

x+18

36+18

54 degree

for angle B

angle B =x

=36 degree

please helppppppppp me​

Answers

So there was a total of 28 games played and the Houston Tigers only scored above 53 points 4 times. Now the fraction would be 4/28 but we have to reduce so the real answer is actually 1/7

plllzzz im new and i neeed help

find the volume of the following composite object. enter your answer as an integer in the box


Answers

Answer:

4082

Step-by-step explanation:

Given

The composite object

Required

The volume

The object is a mix of a cone and a hemisphere

Such that:

Cone

[tex]r = 10cm[/tex] ---- radius (r = 20/2)

[tex]h = 19cm[/tex]

Hemisphere

[tex]r=10cm[/tex]

The volume of the cone is:

[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

[tex]V_1 = \frac{1}{3}\pi * 10^2 * 19[/tex]

[tex]V_1 = \frac{1900}{3}\pi[/tex]

The volume of the hemisphere is:

[tex]V_2 = \frac{2}{3}\pi r^3[/tex]

[tex]V_2 = \frac{2}{3}\pi 10^3[/tex]

[tex]V_2 = \frac{2000}{3}\pi[/tex]

So, the volume of the object is:

[tex]V = V_1 + V_2[/tex]

[tex]V = \frac{1900}{3}\pi + \frac{2000}{3}\pi[/tex]

[tex]V = \frac{3900}{3}\pi[/tex]

[tex]V = 1300\pi[/tex]

[tex]V = 1300 * 3.14[/tex]

[tex]V = 4082[/tex]

Ariana owns a food truck that sells tacos and burritos. She sells each taco for $4 and each burrito for $8.25. Ariana must sell at least $960 worth of tacos and burritos each day. Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.

Answers

Answer:

09

Step-by-step explanation:

The given polygons are similar.
Find the value of x.

Answers

Answer: 6x−6

6x−6

=6(x−1)

Answer:

6(x−1)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

1.Ramu deposited Rs. 10,000 in a bank where interest is compounded
half yearly. If the rate of interest is 10% annually. How much amount he
will get after a year?
3​

Answers

Answer:

Future value, A = $10,500

Step-by-step explanation:

Given the following data;

Principal = Rs. 10,000

Interest rate compounded half yearly = 10% = 10/2 = 5%

Time = 1 year

To find the future value, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{100})^{t}[/tex]

Where;

A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.

Substituting into the equation, we have;

[tex] A = 10000(1 + \frac{5}{100})^{1}[/tex]

[tex] A = 10000(1 + 0.05)[/tex]

[tex] A = 10000(1.05)[/tex]

Future value, A = $10,500

CGB=79 the what is DGB

Answers

Answer:

101

Step-by-step explanation:

Angles 1 and 2 together equal 180, Angle 1 is 79 therefore

180 = Angle 1 + Angle 2

180 = 79 + Angle 2

180 - 79 = Angle 2

101 = Angle 2

Someone help me please
whats the square root of 9 over 16

Answers

Answer:

± [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{\frac{9}{16} }[/tex] = [tex]\frac{\sqrt{9} }{\sqrt{16} }[/tex] = ± [tex]\frac{3}{4}[/tex] ← note plus or minus

Answer:

3/4

Step-by-step explanation:

The square root of 9 is 3 and the square root of 16 is 4 so you get an answer of 3/4.

Hope it helps

The graph of g(x) resembles the graph of f(x) = x2, but it has been changed.
Which of these is the equation of g(x)?

Answers

Answer:

B. g(x)=x²-3 b is my answer

write three ratios equivalent to the given ration 7/2

Answers

Answer:

(7*2 / 2*2) = 14/4 = 3.5

(7*3 / 2*3) = 21/6  = 3.5

(7*4 / 2*4) = 28/8 = 3.5

Step-by-step explanation:

just multiply or divide both number by the same quantity and you will maintain the ratio

Mia cut a piece of felt into 3 equal
sections. She used 1 section for an art project. What fraction of the felt did Mia use for the art
project?
(1 Point)

Answers

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

Mia used One Third of the felt for her art project. 3/3 would be the whole felt together. Since one part of three sections was used up then this means that 1/3 was used.

The sales tax for an item was $6.40 and it cost $320 before tax.
Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

2%

Step-by-step explanation:

Find the sales tax rate by dividing the amount of sales tax by the original cost:

6.40/320

= 0.02

So, the sales tax rate is 2%

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