1. The problem statement, all variables and given/knowndata Problem 1. A block h
ID: 1743225 • Letter: 1
Question
1. The problem statement, all variables and given/knowndataProblem 1. A block having mass m and charge +Q is connected toan
insulating spring havingforce constant k. The block lies on a frictionless, insulatinghorizontal track, and the system is immersed in auniform electricfield of magnitude E directed as shown in Figure
P25:7. The block is released from rest at a moment when the springis unstretched (that is, when x = 0).
(a) By what maximum amount does the spring expand?
(b) What is the equilibrium position of the block?
Problem 2. Consider a closed surface S in a region of gravitationalfield g. Gauss’s law for gravitationtells us that the gravitational flux through surface S is linearlyproportional to the total mass min occupying the volume containedby S. More specifically, Gauss’s law states that
(closedintegral)g x da =-4Gmin :
Note that g here is the total electricfield, due to mass sources both inside and outside S. The value ofG, the gravitational constant, is about 6.673x10-11 N m2/kg2.
(a) Earth’s volume mass density, at any distance r from itscenter, is given approximately by the function p = A-Br=R, where A= 1.42 x 104 kg/m3, B = 1.16 x104 kg/m3, and Earth’s radius R =6.370 x 106 m. Calculate the numerical value ofEarth’s mass M. Hint: The volume of a
spherical shell, lying between radii r and r + dr, is dv =4(pie)r2dr.
(b) Determine the gravitational field inside Earth.
(c) Using the result of part b, determine the gravitational fieldmagnitude at Earth’s surface.
2. Relevant equations
3. The attempt at a solution
1.Arbitrarily choose V = 0 at 0. Then at other points
V= Ex and Ue =QV=QEx.
Between the endpoints of the motion,
(K +Us+ Ue)i = (K+Us +Ue)f
0+0+0=0+(1/2)kx2max QExmax soxmax = (2QE)/k
At equilibrium,
Fx= Fs+Fe= 0 or kx =QE .
So the equilibrium position is at x = QE/k
Problem 2. I have no clue at where to begin, or what equations touse. Any help is appreciated.
Explanation / Answer
can anyone help me with number 2?
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