516 Solutions Manual
P
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 517
Problem 3.72
The small object of mass
m
is placed on the rotating conical surface at the radius shown. If the coefficient
of static friction between the object and the rotating surface is 0.8, calculate the maximum angular velocity
!c
of the cone about the vertical axis for which the object will not slip. Assume the
!c
is increased very
gradually so that the angular acceleration of the cone can be ignored.
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.
518 Solutions Manual
P
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 519
Problem 3.73
The wedge-shaped cart
B
is moving to the left with acceleration
aB
. The coefficient of static friction between the crate and the cart
is insufficient to prevent slipping between the two. If the mass of
A
is
m
and the coefficient of kinetic friction between the crate and the
cart is
k
, determine the acceleration of the crate in the component
system shown.
Solution
520 Solutions Manual
Problem 3.74
The cutaway of the gun barrel shows a projectile moving through
the barrel. If the projectile’s exit speed is
vsD1675 m=s
(relative
to the barrel), the projectile’s mass is
18:5 kg
, the length of the
barrel is
LD4:4
m, the acceleration of the projectile down the
gun barrel is constant, and
✓
is increasing at a constant rate of
0:18 rad=s, determine
(a) The acceleration of the projectile.
(b) The pressure force acting on the back of the projectile.
(c) The normal force on the gun barrel due to the projectile.
as the projectile leaves the gun, but while it is still in the barrel.
Assume that the projectile exits the barrel when
✓D20ı
, and
ignore friction between the projectile and the barrel.
Solution
Part (a) of the problem consists of a purely kinematics question. By contrast, Parts (b) and (c) entail the
computation of forces and the use of Newton’s second law. We solve Part (a) first and then we will use the
Dynamics 2e 521
Parts (b) and (c).
We model the projectile as a particle subject
only to its own weight
mg
, the force
P
due to the pressure acting
522 Solutions Manual
Problem 3.75
A simple sling can be built by placing a projectile in a tube and then spinning
it. Consider a simple model in which the tube is pinned as shown and is
rotated about the pin in the horizontal plane at constant angular velocity !.
Assume that there is no friction between the projectile and the inside of the
tube and that the projectile is initially kept fixed at a distance
d
from the
open end of the tube.
After the projectile is released, compute the normal force exerted by the
inside of the tube on the projectile as a function of position of the projectile
along the tube.
Solution
The contact between the projectile and the tube has negligible friction and the
motion of the projectile is in the horizontal plane. Because we are neglecting
Dynamics 2e 523
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524 Solutions Manual
Problem 3.76
A simple sling can be built by placing a projectile in a tube and then spinning
it. Consider a simple model in which the tube is pinned as shown and is
rotated about the pin in the horizontal plane at constant angular velocity !.
Assume that there is no friction between the projectile and the inside of the
tube and that the projectile is initially kept fixed at a distance
d
from the
open end of the tube.
Letting
dD3ft
and
LD7ft
, determine the value of the tube’s angular
velocity
!
if, after release, the projectile exits the tube with a speed of
90 ft=s.
Solution
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Dynamics 2e 525
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.