506 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 507
Problem 3.67
Revisit Example 3.7 and assume that the trajectory of the ball is shallow enough that the effects of the
drag force in the
y
direction can be neglected and that the component of the drag force in the
x
direction
is proportional to the square of the
x
component of velocity. Using this assumption and the same drag
coefficient discussed in the example (
CdD4:71⇥107lbs2=ft2
), compute the horizontal distance
R
traveled by a
1:61 oz
golf ball subject to the same initial conditions given in the example, i.e., the initial
velocity has a magnitude v0D187 mph and an initial orientation ✓0D11:2ı.
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.
508 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 509
Problem 3.68
Using a cylindrical component system whose origin is at the center of curvature of the path of the car,
derive the governing equations for Example 3.8 on p. 198. Solve the equations and verify that you get the
same solution.
Solution
As was done in Example 3.8 on p. 198 of the textbook, and referring to the FBDs at the
510 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 511
Problem 3.69
A race car is traveling at a constant speed over a circular banked turn. Oil
on the track has caused the static friction coefficient between the tires and
the track to be
sD0:2
. If the radius of the car’s trajectory is
⇢D320
m
and the bank angle is
✓D33ı
, determine the range of speeds within which
the car must travel not to slide sideways.
Solution
512 Solutions Manual
We now consider the case with
vDvmin
. Referring to the FBD at the right, we model
the car as as was done previously. However, the force
F
is directed to the left and upward
Dynamics 2e 513
Problem 3.70
A race car is traveling at a constant speed
vD200 mph
over a circular banked turn. Let the weight of the
car be
WD4000 lb
, the radius of the car’s trajectory be
⇢D1100 ft
, the bank angle be
✓D33ı
, and the
coefficient of static friction between the car and the track be
sD1:7
. Determine the component of the
friction force perpendicular to the direction of motion.
Solution
514 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 515
Problem 3.71
Revisit Example 3.9 on p. 200 by letting the sphere be released at
✓D0
with a speed
v0D0:5 m=s
.
Neglecting friction, compute the angle at which the sphere separates from the cylinder if RD1:35 m.
Solution