In outer space rock 1, with mass 3 kg and velocity < 3900, -2700, 3600 > m/s, struck rock 2, which was at rest. after the collision, rock 1's velocity is < 3500, -2000, 4100 > m/s.

suppose the collision was elastic (that is, no change in kinetic energy and therefore no change in thermal or other internal energy of the rocks). in that case, after the collision, what is the kinetic energy of rock 2?

on the other hand, suppose that in the collision some of the kinetic energy is converted into thermal energy of the two rocks, where ethermal,1 + ethermal,2 = 2.52106 j. what is the final kinetic energy of rock 2?

in this case (some of the kinetic energy being converted to thermal energy), what was the transfer of energy q (microscopic work) from the surroundings into the two-rock system during the collision? (remember that q represents energy transfer due to a temperature difference between a system and its surroundings.)

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2