The "spring-flex" exercise system consists of a spring with one end fixed and a handle on the other end. The idea is that you exercise your muscles by stretching the spring from its natural length, which is 38 cm. If a 110 Newton force is required to keep the spring stretched to a length of 58 cm, how much work is required to stretch it from 50 cm to 74 cm?

Q: What is the force on a 1000kg elevator accelerating at 2 m/s

A:

Q: A spring with an mm-kg mass and a damping constant 4 (kg/s) can be held stretched 2 meters beyond…

A: Given that, the damping constant 4kg/s, stretched length x=2 meter and force is F=6  Newtons. Find…

Q: A force of 7 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How…

A: Given that 7 pounds is required to stretch 0.2 ft

Q: A spring has a natural length of 20 cm. If a force of 25 N is required to keep it stretched to a…

A: To determine the work required to stretch the spring from 22 cm to 37 cm.

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

A: Given problem Given that   As you are walking in the forest you look up just as a boulder becomes…

Q: It takes 120 J of work to stretch a spring 0.5 m from its equilibrium position. How much work is…

A: Consider the given values and the formula for the work in integral form. Work=W=120…

Q: 4. Saturn has mass 95 times that of the Earth and 9.5 times of its radius. From this data, (a)…

A:

Q: Suppose the ball is dropped at rest from the top of the house 64 ft above the ground and the only…

A:

Q: Work of 3 Joules is done in stretching a spring from its natural length to 11 cm beyond its natural…

A: Given information: work done  is 3 joules and the natural length is 11 cm Spring stretched t the…

Q: If a 6-kg bowling ball is rolled down the bowling lane with a force of 12n, what is the acceleration…

A:

Q: A force of 10 Ib is required to hold a spring stretched 4 feet beyond its natural length. How much…

A:

Q: A 6.3-kg box is being lifted by means of a light rope that is threaded through a single, light,…

A: h = 1.5 mt = .42 sh = 1/2 * a * t^2====> a = 2h / t^2 = 3 / .1764 = 17.00 m/s^2final velocity, v…

Q: Work of 22 Joules is done in stretching a spring from its natural length to 20 cmcm beyond its…

A:

Q: A boat with its load weighs 1,328 N. If the force exerted upon the boat by the motor in the…

A:

Q: A stream of water flowing horizontally with a speed of 15ms- gushes out of a tube of cross-sectional…

A: Given that, A stream of water flowing horizontally with speed               v=15ms-1 and area of…

Q: How much work is done when a hoist lifts a 270-kg rock to a height of 4 m? (Use 9.8 m/s2 for the…

A:

Q: The "spring-flex" exercise system consists of a spring with one end fixed and a handle on the other…

A: Given: 110110 N force is required to stretch,The spring from it's natural length of 3838 cm to a…

Q: Work of 2 Joules is done in stretching a spring from its natural length to 17 cm beyond its natural…

A:

Q: 4 Joules of work are done when stretching a spring from its natural length to 20 cm beyond its…

A: The force needed to stretch the spring from its natural length to x meter is  F=kx Work done  by…

Q: 4 Joules of work are done when stretching a spring from its natural length to 14 cm beyond its…

A: Given that:   4 Joules of work are done when stretching a spring from its natural length to 14 cm…

Q: A force of 3.0 pounds is needed to stretch the spring to 1.0 ft. from its natural length of 10…

A: Given problem:- A force of 3.0 pounds is needed to stretch the spring to 1.0 ft. from its natural…

Q: A force of 4 lb is required to hold a spring stretched 0.5 ft beyond its natural length. How much…

A:

Q: A force of 4 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How…

A:

Q: You throw a ball (from ground level) of mass 1 kilogram upward with a velocity of v = 27 m/s on…

A:

Q: If a force of 5 lb produces a stretch of one - tenth the natural length L ft of a spring , how much…

A:

Q: A 500-lb motorcycle is headed up a hill inclined at 12°. What force is required to keep the…

A:

Q: Work of 3 Joules is done in stretching a spring from its natural length to 17 cm beyond its natural…

A: Given  Work = 3 Joule  Distance= 17cm = 0.17m  Find force .

Q: Suppose that when launching an 800-kg roller coaster car an electromagnetic propulsion system exerts…

A: ork done by the force in travelling 60 m isW=∫060 F dx

Q: . A spring has a natural length of 40 cm. If a 60-N force is required to keep the spring compressed…

A: Given natural length of spring , l=40 cmFor a change in length , △x of 10 cm , 60 N force is…

Q: 1) What is the force on a 1000 kg elevator accelerating at 2 m/s2?

A: Force = mass * acceleration.

Q: a large gear with 42 rotates at 25 rpm. it turns a small gear with 14 teeth. how fast does the small…

A:

Q: A force of 200 N will stretch a garage door spring 0.8 m beyond its unstressed length. How far will…

A: Given information:

Q: Shown is the graph of a force function (in newtons) that increases to its maximum value and then…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Suppose a spring has a natural length of 18 inches. If a force of 20 lbs is required to stretch and…

A: Use the integration to find the work performed to stretch the spring.

Q: When a particle is located at a distance x feet from the origin, a force of x +2x pounds acts on it.…

A: We have the given Force function F(x) = x2 + 2x where x is the distance in feet from the origin.…

Q: A cable with mass 2 kg/meter is lifting a load of 150 kg that is initially at the bottom of a…

A: Mass = 150 kg, We know that, g = 9.81 ms2

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

A: Given that the acceleration due to gravity is a=32 ft/sec2. The head is 200 ft below the base of the…

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Compress from the natural length through 1-0.8= 0.2 meter spring constant 'k'=16 N/m

Q: How much force in N is required to lift a box that weighs 8 kg? Use the fact that acceleration due…

A:

Q: A spring's natural length is 10 m. If it requires 5 J to stretch the spring from 13 m to 17 m, find…

A: Given: spring's natural length is 10 m. I.e x0 = 10 m  When the spring is stretched it's length…

Q: When Apollo 15 astronaut David Scott dropped a hammer and a feather on the moon to demonstrate that…

A: An astronaut dropped a hammer and feather on the moon.These are dropped from about 4 ft above the…

Q: Work of 5 Joules is done in stretching a spring from its natural length to 17 cm beyond its natural…

A:

Q: A chain 71 meters long whose mass is 26 kilograms is hanging over the edge of a tall building and…

A:

Q: rce of 40 N is required to hold a spring that has been stretched from natural length of 10 cm to a…

A:

Q: If 24 J of work are needed to stretch a spring from 15 cm to 19 cm and 40 J are needed to stretch it…

A:

Q: Use the fact that 1 m3 = 1000 liter, and show that 1ml = 1 cm3

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: A boat with its load weighs 1,500 N. If the force exerted upon the boat by the motor in the…

A:

Q: A force of 6 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How…

A: F = -kx  6 = -k(0.2) So, k = 30   Work done, W = (1/2)kx2 = (1/2)*(30)*(0.9)2 = 12.15

Q: If a force of 50 pounds is required to stretch a spring by 1 inch from its natural length of 10…

A:

Q: A force of 55 pounds is required to hold a spring that is stretched 0.5 feet beyond its natural…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.