Calculate the work required to stretch the following springs 1.25 m from their equilibrium positions. Assume Hooke's law is obeyed. a. A spring that requires 100 J of work to be stretched 0.5 m from its equilibrium position. b. A spring that requires a force of 250 N to be stretched 0.5 from its equilibrium position.

Calculate the work required to stretch the following springs 0.4 m from their equilibrium positions. Assume Hooke’s law is obeyed. A spring that requires 2 J of work to be stretched 0.1 m from its equilibrium position

a. It takes 50 J of work to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m? b. It takes 50 N of force to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m?

Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hooke's law is obeyed. a. A spring that requires a force of 50 N to be stretched 0.2 m from its equilibrium position. b. A spring that requires 50 J of work to be stretched 0.2 m from its equilibrium position.

It takes 50 J of work to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m?

Calculate the work required to stretch the following springs 1.25 m from their equilibrium positions. Assume Hooke’s law is obeyed. A spring that requires 100 J of work to be stretched 0.5 m from its equilibrium position

Calculate the mass and centroid (center of mass) of the following thin plate, assuming constant density.

The region bounded by $y=\ln x$, the $x$-axis, and $x=e$

Calculate the mass and centroid (center of mass) of the following thin plate, assuming constant density.

The region bounded by $y=1-|x|$ and the $x$-axis

A 30-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain has a density of 5 kg/m.

How much work is required to wind the entire chain onto the cylinder using the winch?

Natural light of irradiance $I_{i}$ is incident normally on an HN-32 polarizer. (a) How much light emerges from it? (b) A second identical polarizer is placed parallel to and behind the first. How much light emerges when the two transmission axes are at $45^{\circ}$?

Calculate the work required to stretch the following springs $0.5 \mathrm{~m}$ from their equilibrium positions. Assume Hooke's law is obeyed. (a). A spring that requires a force of $50 \mathrm{~N}$ to be stretched $0.2 \mathrm{~m}$ from its equilibrium position. (b). A spring that requires $50 \mathrm{~J}$ of work to be stretched $0.2 \mathrm{~m}$ from its equilibrium position.

Suppose a force of 30 N is required to stretch and hold a spring 0.2 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.4 m from its equilibrium position? c. How much work is required to stretch the spring 0.3 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.2 m if it has already been stretched 0.2 m from its equilibrium position?

A spring on a horizontal surface can be stretched and held $0.5 \mathrm{~m}$ from its equilibrium position with a force of $50 \mathrm{~N}$. (a). How much work is done in stretching the spring $1.5 \mathrm{~m}$ from its equilibrium position? (b). How much work is done in compressing the spring $0.5 \mathrm{~m}$ from its equilibrium position?

A 60-m-long, 9.4-mm-diameter rope hangs free from a ledge. The density of the rope is 55 g/m. How much work is needed to pull the entire rope to the ledge?