You’re an engineer for a company that makes bungee-jump cords and you’re asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force-distance relations described by F = −( kx + bx2 + cx3 + dx4) where k, b, c, and d are constants.
a) How will you model this problem?
b. Given a cord with un-stretched length 4, what is the formula for the work done?
c. Evaluate the work done in doubling the stretch of an 8 m cord with k= 420N/m, b = -86N/m2, c = 12N/m3, and d=-0.50N/m4

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island

The uniform slender bar rests on a smooth horizon- tal surface when a force f is applied normal to the bar at point a. point a is observed to have an initial acceleration aa of 20 m/s2, and the bar has a corre- sponding angular acceleration of 18 rad /s2. deter- mine the distance b.