Amass m fixed to a spring oscillates between limits −a ≤ x ≤ a subject to hooke’s law f = −mω2 x . as it moves back and forth, you take many photographs at random intervals. on each picture you measure the distance the mass has moved. a. find the probability density ρ(x) for finding the mass is at a position x in a random picture. b. sketch ρ(x) and interpret the result. where is ρ(x) largest and where is it smallest? c. what is the average position of the mass? explain your result. d. what is the standard deviation from the mean of the mass? e. how does your result for part d compare to a uniform motion at constant speed in the range −a ≤ x ≤ a ? explain why this makes sense.

5g of ammonium nitrate was dissolved in 60g of water in an insulated container. the temperature at the start of the reaction was 23.0°c and at the end it was 19.0°c. calculate the energy absorbed by the reaction.

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r