PHYS 204A Midterm: PHYS 204A Chico State Exams Exam 4 Spring 18

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turquoisegnu128

31 Jan 2019

School

Chico State University

Department

Physics

Course

PHYS 204A

Professor

All

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Document Summary

V = vi + at x = xi + vit + 2 at2 v2 = v2 i + 2a x. R = v2 sin(2 ) g dv dt d2x dt2 a x = r cos( ) y = r sin( ) r = px2 + y2 tan( ) = y x. Six points each: draw free-body diagrams for the following two situations: (a) paul"s jet airplane is taking o from a horizontal runway. Friction is negligible, air drag is not. (b) flor is on a bridge and throws a rock straight down towards the water. The rock has just been released: ken"s spaceship, with mass m = 8. 0 104 kg, is at rest in deep space. Its thrusters provide a force of 1200 kn. Ken res the thrusters for 20 s, then coasts for 12 km. 3: vaneza"s 4,000 kg truck is parked on a 15 slope. What is the tension in the string? m,r m m.

Related Questions

An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq.

(a) At a point P, which is far from the dipole (r >> a), show that the electric potential is

V =Kp cos θ /r²

(b) Calculate the radial component E_r and the perpendicular component E_θ of the associated electric field. Note that E_θ = —(1/r) (∂V/∂r). Do these results seem reasonable for

(c) θ = 90° and 0°?

(d) For r= 0?

(e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r= (x² + y²)^1/2 and cosθ =y /(x² + y²)^1/2

and

(f) Using these results and again taking r>> a, calculate the field components; E_x and E_y.

harlequintiger488

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

Parametric equations for a general Keplerian orbit are r(Ï) = a(1 â e cosÏ)

t(Ï) = *(T)/2Ï+ ( Ïâ e sinÏ)

tan(Ï/2) = *(1+e)/(1âe)+1/2 tan(Ï/2)

Here Ï is an independent variable. The solution is periodic in Ïwith period âÏ = 2Ï. Also, a, e, T are constants that determine theparameters of the orbit.

Figure 2 shows the relation between Ï and the spatialcoordinates. In the figure, the coordinates (Î¾,Î·) are defined by Î¾= x + ae and Î· = y a /b,

withb=a*1âe2 ]1/2.

(A) What kind of curve is the orbit?

(D) Determine Î¾(Ï) and Î·(Ï).

(E) Express r as a function Ï .

(F) The angular momentum is L = m r2dÏ/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(dÏ/dt)2â 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.

1) A flying pig (wings not shown) of mass m, supported from theceiling by a string, travels at speed v -- just the right speedthat it doesn't go up or down; it travels in a horizontal circle ina plane parallel to the ground.
c) On the pig at right, draw a force diagram showing the two forcesacting on the pig. Donât draw the components yet.
d) One force is diagonal and one force is vertical. Which do wechoose for an axis? We'll choose horizonal/vertical. Why not choosethe string and a line perpendicular to the string?
e) Given that we're choosing the radius and up/down line for ouraxis, which force needs to be resolved into components?
f) Using letters only, write the force equation for the up/downaxis in terms of FT, Î¸, m and g (Correct answer: FtCos(Î¸)=mg)
g) Using letters only, write the force equation for the radius axisin terms of FT, Î¸, m,v and r. (Correct answer:Ftsin(Î¸)=(mv^2/r)
h) Combine them into one equation using everybody's favorite trigidentity. (No, not sin(2Î¸) = 2sin(Î¸)cos(Î¸).) The equation shouldread: tan(Î¸) = v^2/rg

PHYS 204A Midterm: PHYS 204A Chico State Exams Exam 4 Spring 18

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Physics: Principles with Applications

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