Consider a spring that does not obey hooke's law very faithfully. one end of the spring is fixed. to keep the spring stretched or compressed an amount x, a force along the x-axis with x-component fx=kx−bx2+cx3 must be applied to the free end. here k=100n/m, b=700n/m2, and c=12000n/m3. note that x> 0 when the spring is stretched and x< 0 when it is compressed.

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.

Power can be defined as a. the distance over which work was done. b. how much work can be done in a given time. c. all the work in an given area. d. the energy required to do work.

14. a body is projected with velocity vi from a.at the same time another body is projectedvertically upwards from point b withvelocity v2 lies vertically below the highestpoint. both the bodies collide thenv2÷v1is