978-0073398242 Chapter 12 Solution Manual Part 15

PROBLEM 12.91 (Continued)

PROBLEM 12.92

Two 2.6-lb collars A and B can slide without friction on a frame, consisting

of the horizontal rod OE and the vertical rod CD, which is free to rotate

about CD. The two collars are connected by a cord running over a pulley

that is attached to the frame at O and a stop prevents collar B from moving.

The frame is rotating at the rate

12 rad/s







and 0.6 ftr when the stop

is removed allowing collar A to move out along rod OE. Neglecting

friction and the mass of the frame, determine, for the position 1.2 ft,r

(a) the transverse component of the velocity of collar A, (b) the tension in

the cord and the acceleration of collar A relative to the rod OE.

PROBLEM 12.93

A small ball swings in a horizontal circle at the end of a cord of length

1

l

,

which forms an angle

1



with the vertical. The cord is then slowly drawn

through the support at O until the length of the free end is

2

.l

(a) Derive a

relation among

1

,l

2

,l

1

,



and

2

.



(b) If the ball is set in motion so that

initially

1

0.8 ml

and

1

35 ,





determine the angle

2



when

2

0.6 m.l

PROBLEM 12.94

A particle of mass m is projected from Point A with an initial velocity

0

v perpendicular to OA and moves under a central force F along an

elliptic path defined by the equation 0/(2 cos ).rr



 Using Eq.

(12.35), show that F is inversely proportional to the square of the

distance r from the particle to the center of force O.

PROBLEM 12.95

A particle of mass m describes the logarithmic spiral 0b

rre



under a central force F directed toward the

center of force O. Using Eq. (12.35) show that F is inversely proportional to the cube of the distance r from

the particle to O.

PROBLEM 12.96

A particle of mass m describes the path defined by the equation

0(6 cos 5)rr





under a central force F directed away from the

center of force O. Using Eq. (12.35), show that F is inversely

proportional to the square of the distance r from the particle to O.

PROBLEM 12.97

A particle of mass m describes the parabola 2

0

4yxrunder a central

force F directed toward the center of force C. Using Eq. (12.35) and

Eq.





12.37 ‘ with 1,





show that F is inversely proportional to the square

of the distance r from the particle to the center of force and that the angular

momentum per unit mass 0

2.hGMr

PROBLEM 12.98

It was observed that during its second flyby of the earth, the Galileo spacecraft had a velocity of 14.1 km/s as

it reached its minimum altitude of 303 km above the surface of the earth. Determine the eccentricity of the

trajectory of the spacecraft during this portion of its flight.

PROBLEM 12.99

It was observed that during the Galileo spacecraft’s first flyby of the earth, its maximum altitude was 600 mi

above the surface of the earth. Assuming that the trajectory of the spacecraft was parabolic, determine the

maximum velocity of Galileo during its first flyby of the earth.

PROBLEM 12.100

As a space probe approaching the planet Venus on a parabolic trajectory reaches

Point A closest to the planet, its velocity is decreased to insert it into a circular

orbit. Knowing that the mass and the radius of Venus are 4.87 24

10 kg and 6052

km, respectively, determine (a) the velocity of the probe as it approaches A,

(b) the decrease in velocity required to insert it into the circular orbit.