978-0073380308 Chapter 3 Solution Manual Part 10

496 Solutions Manual

Problem 3.61

Continue Prob. 3.60 and using mathematical software, numerically

solve the equations of motion. Use the same parameters and initial

conditions that were used in Example 3.10, and compare your

results with those presented in that example.

Solution

Referring to the FBD on the right, we model the disk as a particle moving in

the horizontal plane and subject only to the spring force

Fs

. We adopt the

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498 Solutions Manual

Problem 3.62

Derive the equations of motion for the pendulum supported by a linear spring of

constant

k

and unstretched length

ru

. Neglect friction at the pivot

O

, the mass of

the spring, and air resistance. Treat the pendulum bob as a particle of mass

m

, and

use polar coordinates.

Solution

Dynamics 2e 499

Problem 3.63

Using mathematical software, solve the equations of motion for the pendulum

supported by a linear spring of constant

k

(derived in Prob. 3.62). Plot the trajectory

of the mass

m

in the vertical plane for a number of different values of

k=m

. The

unstretched length of the spring is

0:25

m, and the mass is released when the

pendulum is vertical, the spring is stretched

0:75

m, and the mass is moving to the

right at 1m=s.

Solution

Referring to the FBD on the right, we model the pendulum bob as a particle subject only

to its own weight

mg

and to the spring force

Fs

. To study the motion of the pendulum

500 Solutions Manual

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Dynamics 2e 501

Problem 3.64

The system shown is initially at rest when the bent bar starts to rotate about the vertical axis

AB

with

constant angular acceleration

˛0D3rad=s2

. The coefficient of static friction between the collar of mass

mD2kg and the bent bar is sD0:35, and the collar is initially dD70 cm from the spin axis AB.

Assuming the motion starts at

tD0

, determine the time at which the collar starts to slip relative to the

bent bar.

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

502 Solutions Manual

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Dynamics 2e 503

Problem 3.65

The system shown is initially at rest when the bent bar starts to rotate about the vertical axis

AB

with

constant angular acceleration

˛0D3rad=s2

. The coefficient of static friction between the collar of mass

mD2kg and the bent bar is sD0:35, and the collar is initially dD70 cm from the spin axis AB.

Determine the number of rotations undergone by the bent bar when the collar starts to slip relative to it.

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

504 Solutions Manual

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Dynamics 2e 505

Problem 3.66

Revisiting Example 3.7, assume that the drag force in the

x

direction is proportional to the square of the

x

component of velocity, but that the ball’s trajectory is shallow enough to neglect the drag force in the

y

direction. Using this assumption, letting

O

be the initial position of the ball, and letting the ball’s initial

velocity have a magnitude

v0

and letting it form an angle

✓0

with the

x

axis, determine an expression for

the trajectory of the ball of the form yDy.x/.

Solution

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.