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PHYS 1021 Chapter 10: Physics for Scientists and Engineers Chapter 10 Notes

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olivehorse317
15 Dec 2017
School
GWU
Department
Physics
Course
PHYS 1021
Professor
Jha

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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(e) (2 points) ?Eint?
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In Fig. 30-39, a wire loop of dimensions L = 42.4 cm and W = 28.2cm lies in a magnetic field . What are the (a) magnitude and (b)direction (clockwise - show "1" , counterclockwise - show "0" or“none” - show "3" if = 0) of the emf induced in the loop if = (6.10× 10-2 T/m)y ? What are (c) (in mV) and (d) the direction if =(6.24 × 10-2 T/s)t ? What are (e) (in mV) and (f) the direction if= (8.31 × 10-2 T/m·s)yt ? What are (g) and (h) the direction if =(3.28 × 10-2 T/m·s)xt ? What are (i) and (j) the direction if =(5.00 × 10-2 T/m·s)yt ?








Figure 1 illustrates a Keplerian orbit, with Cartesiancoordinates (x,y) and polar coordinates (r,φ).

Parametric equations for a general Keplerian orbit are r(ψ) = a(1 − e cosψ)

t(ψ) = *(T)/2π+ ( ψ− e sinψ)

tan(φ/2) = *(1+e)/(1−e)+1/2 tan(ψ/2)

Here ψ is an independent variable. The solution is periodic in ψwith period ∆ψ = 2π. Also, a, e, T are constants that determine theparameters of the orbit.

Figure 2 shows the relation between ψ and the spatialcoordinates. In the figure, the coordinates (ξ,η) are defined by ξ= x + ae and η = y a /b,

withb=a*1−e2 ]1/2.

(A) What kind of curve is the orbit?

(C) Determine x(ψ) and y(ψ).

(D) Determine ξ(ψ) and η(ψ).

(E) Express r as a function φ .

(F) The angular momentum is L = m r2dφ/dt. Determine L in termsof {a,e,T} Hence verify that L is a constant of the motion.

(G) The energy isE = [1/2] m ( dr/dt )2+ [1/2] m r2(dφ/dt)2− GMm/r.Determine E in terms of {a,e,T}.

(H) E must be a constant of the motion. Hence determine T and Efrom the equation that you obtained in (F).

(I) Write T in terms of the spatial orbit parameters and theforce constant GM.

(J) Now express L and E in terms of a, e, GM.

(K) In Figure 1, determine the coordinates of the points P, A,and R

(L) In Figure 1, determine the time t at the point R.