Ablock of mass m is projected straight upward by a strong spring whose stiffness is ks. when the block is a height y1 above the floor, it is traveling upward at speed v1, and the spring is compressed an amount s1. a short time later the block is at height y2, traveling upward at speed v2, and the spring is compressed an amount s2. in this discussion we'll use the energy principle in the form ef = ei + wext, where we assume that thermal transfer of energy (microscopic work) q between the block and the air is negligible. we can ignore the rest energies which don't change, and the kinetic energy of the earth, which hardly changes. i. system: universe (block + spring + earth) for the system consisting of the block, the spring, and the earth, which of the following equations correctly represents the energy principle in the form ef = ei + wext? (1/2)mv22 - (1/2)kss22 = (1/2)mv12 - (1/2)kss12 - mg(y2-y1)(1/2)mv22 + (1/2)kss22 = (1/2)mv12 + (1/2)kss12 - mg(y2-y1)(1/2)mv22 - mgy2 + (1/2)kss22 = (1/2)mv12 - mgy1 + (1/2)kss12(1/2)mv22 = (1/2)mv12 - (1/2)ks(s22 - s12) - mg(y2-y1)(1/2)mv22 = (1/2)mv12 + (1/2)ks(s22 - s12) + mg(y2-y1)(1/2)mv22 + mgy2 + (1/2)kss22 = (1/2)mv12 + mgy1 + (1/2)kss12

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

What are igneous intrusions and extrusions

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) .