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Dynamics 2e 757
Problem 4.68
Spring scales work by measuring the displacement of a spring that supports
both the platform and the object, of mass
m
, whose weight is being measured.
Neglect the mass of the platform on which the mass sits, and assume that the
spring is uncompressed before the mass is placed on the platform. In addition,
assume that the spring is linear elastic with spring constant
k
. You may have
solved these same problems using Newton’s second law when doing Prob. 3.27
and 3.28 — here use the work-energy principle to solve them.
If the mass
m
is gently placed on the spring scale (i.e., it is dropped from
zero height above the scale), determine the expression for maximum velocity
attained by the mass mas the spring compresses.
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.
758 Solutions Manual
Problem 4.69
A
6lb
collar is constrained to travel along a rectilinear and friction-
less bar of length
LD5ft
. The springs attached to the collar are
identical, and they are unstretched when the collar is at
B
. Treat-
ing the collar as a particle, neglecting air resistance, and knowing
that at
A
the collar is moving to the right with a speed of
11 ft=s
,
determine the linear spring constant
k
so that the collar reaches
D
with zero speed. Points Eand Fare fixed.
Solution
We denote the positions of the collar at
A
and
D
by
¿
and
¡
, respectively. Between
these two positions, we model the collar as a particle subject to its own weight
mg
, the
Dynamics 2e 759
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.
760 Solutions Manual
Problem 4.70
A
3kg
collar is constrained to travel in the horizontal plane along a frictionless
ring of radius
RD0:75
m. The spring attached to the collar has a spring constant
kD21 N=m
. Treating the collar as a particle, neglecting air resistance, and
knowing that at
A
the collar is at rest, determine the spring’s unstretched length if
the collar is to reach point Bwith a speed of 2m=s.
Solution
We denote the positions of the collar at
A
and
B
by
¿
and
¡
, respectively. Between
these two positions, we model the collar as a particle subject to the normal reaction
Dynamics 2e 761
Problem 4.71
The truck comes to a stop under the action of a constant braking
force. During braking, either the crate slides or it does not. Con-
sidering the work-energy principle applied to the truck during
braking, will the truck stop in a shorter distance (or time) if the
crate slides, or will the distance (or time) be shorter if it does not
slide? Assume that the truck bed is long enough that you don’t
have to worry about whether or not the crate hits the truck. Justify
your answer.
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.
762 Solutions Manual
Problem 4.72
Consider a pulley system in which bodies
A
and
B
have masses
mAD
2kg
and
mBD10 kg
. If the system is released from rest, neglecting all
sources of friction, as well as the inertia of the pulleys, determine the
speeds of Aand Bafter Bhas displaced a distance of 0:6 m downward.
Solution
Referring to the figure on the right, we model
A
and
B
as particles
subject to the their respective weights,
mAg
and
mBg
and the tension
Dynamics 2e 763
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.
764 Solutions Manual
Problem 4.73
A
700 lb
floating platform is at rest when a
200 lb
crate is thrown
onto it with a horizontal speed
v0D12 ft=s
. Once the crate stops
sliding relative to the platform, the platform and the crate move
with a speed
vD2:667 ft=s
. Neglecting the vertical motion of
the system, as well as any resistance due to the relative motion of
the platform with respect to the water, determine the distance that
the crate slides relative to the platform if the coefficient of kinetic
friction between the platform and the crate is kD0:25.
Solution
We model the platform, of mass
mp
, and the crate, of mass
mc
, as a system of two
particles subject only to their combined weight
.mcCmp/g
and force due to the
Dynamics 2e 765
Problem 4.74
Blocks
A
and
B
, weighing 7 and
15 lb
, respectively, are released from rest
when the spring is unstretched. If all sources of friction are negligible and
kD12 lb=ft
, determine the maximum vertical displacement of
B
from the
release position, assuming that
A
never leaves the horizontal surface shown and
the cord connecting Aand Bis inextensible.
Solution
Referring to the FBD at the right, we model blocks
A
and
B
as a system of particles
subject to their respective weights
mAg
and
mBg
, the force of the spring
Fs
, the
766 Solutions Manual
Problem 4.75
Crates
A
and
B
of mass
50 kg
and
75 kg
, respectively, are released from rest.
The linear elastic spring has stiffness
kD500 N=m
. Neglect the mass of the
pulleys and cables and neglect friction in the pulley bearings.
If
kD0
and the spring is initially unstretched, determine the speed of
B
after Aslides 4m.
Solution
