If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?

A spring has a natural length of 10 cm. It takes 2 J to stretch the spring to 15 cm. How much work would it take to stretch the spring from 15 cm to 20 cm?

If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?

A student measures the amount of stretch of an elastic band under increasing applied forces (a) Graph these data on a force-stretch-distance graph. (b) Use the graph to determine the average spring constant of the elastic band in newtons per metre.

In a steam engine the pressure P and volume V of steam satisfy the equation PV^1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its sur roundings.) Calculate the work done by the engine during a cycle when the steam starts at a pressure of 160 lb/in^2 and a volume of 100 in^3 and expands to a volume of 800 in^3.

A spring has a natural length of 10 cm. It takes 2 J to stretch the spring to 15 cm. How much work would it take to stretch the spring from 15 cm to 20 cm?

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is 1000 kg/m^3.)

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

$$y = √x, y = x^2;$$

about y = 2

A spring requires 5 J to stretch the spring from 8 cmto 12 cm, and an additional 4 J to stretch the spring from 12 cm to 14 cm. What is the natural length of the spring?

A roller coaster car begins at rest at the top of the first hill. Draw a sketch of a roller coaster with a second hill where the roller coaster cannot reach the top. Draw a sketch of a different roller coaster with a second hill that the roller coaster can get over.

A force of $20\text{ N}$ is required to stretch a spring $3\text{ cm}$ beyond its natural length of $24\text{ cm}$. Find the work required to stretch the spring from $30$ to $35\text{ cm}$.

Choose the answer that best describes the action or situation.

Something that would most likely be premeditated

a. a reflex

b. a rainstorm

c. a trip

d. a sneeze

The force $F$ required to stretch a spring varies directly with the BAUUSY J Beer amount the spring is stretched s. Eight pounds is needed to stretch a spring 8 inches. a. Write a direct variation equation that relates F and s. - ~ bB. How much force 1s required to stretch a spring 25 inches?

A spring is suspended vertically from the ceiling of a room. When a mass is attached to the bottom of the spring, the amount of stretch is recorded. A plot of stretch versus mass is given in FIGURE . Use the data given in the plot to determine the force constant of the spring.