Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Dynamics 2e 677
Problem 4.10
Consider a
1500 kg
car whose speed is increased by
45 km=h
over a
distance of 50 m while traveling up an incline with a 15% grade.
Modeling the car as a particle, determine the work done on the car
if the car starts from rest.
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.
678 Solutions Manual
Problem 4.11
Consider a
1500 kg
car whose speed is increased by
45 km=h
over a
distance of 50 m while traveling up an incline with a 15% grade.
Modeling the car as a particle, determine the work done on the car
if the car has an initial speed of 60 km=h.
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.
Dynamics 2e 679
Problem 4.12
The crate moves up the incline a distance
dD4:5 ft
due to the action of the
constant force
PD100 lb
. The weight of the crate is
WD65 lb
, and the
spring with constant
kD10 lb=ft
is unstretched before the crate starts moving.
Friction between the crate and the incline is negligible, and the angle between
the force Pand the surface on which the crate slides is ˇD30ı.
Letting
✓D0ı
, that is, the surface is horizontal, determine the total work
done by all forces after the crate has moved the distance d.
Solution
At the right we show the crate’s FBD along with a sketch of the
coordinate system we will use and the indication of the positions
680 Solutions Manual
Problem 4.13
The crate moves up the incline a distance
dD4:5 ft
due to the action of the
constant force
PD100 lb
. The weight of the crate is
WD65 lb
, and the
spring with constant
kD10 lb=ft
is unstretched before the crate starts moving.
Friction between the crate and the incline is negligible, and the angle between
the force Pand the surface on which the crate slides is ˇD30ı.
Letting
✓D30ı
, determine the total work done by all forces after the crate
has moved the distance d.
Solution
At the right we show the crate’s FBD along with a sketch of the
coordinate system we will use with an indication of the positions
Dynamics 2e 681
Problem 4.14
A
350 kg
crate is sliding down a rough incline with a constant speed
vD7m=s
.
Assuming that the angle of the incline is
✓D33ı
and that the only forces acting on
the crate are gravity, friction, and the normal force between the crate and the incline,
determine the work done by friction over every meter slid by the crate.
Solution
At the right we sketched the FBD of the crate and a coordinate system
for use the solution. We model the crate as a particle subject to its
682 Solutions Manual
Problem 4.15
A vehicle Ais stuck on the railroad tracks as a train Bapproaches with a speed of 120 km=h. As soon as
the problem is detected, the train’s emergency brakes are activated, locking the wheels and causing the
train’s wheels to slide relative to the tracks. If the coefficient of kinetic friction between the wheels and the
track is 0.2, use the work-energy principle to determine the minimum distance
dmin
at which the brakes
must be applied to avoid a collision under the following circumstances:
(a) The train consists of just a 195;000 kg locomotive.
(b)
The train consists of a
195;000 kg
locomotive and a string of cars whose mass is
10⇥106kg
, all of
which can apply brakes and lock their wheels.
(c)
The train consists of a
195;000 kg
locomotive and a string of cars whose mass is
10⇥106kg
, but only
the locomotive can apply its brakes and lock its wheels.
Treat the train as a particle, and assume that the railroad tracks are rectilinear and horizontal.
Solution
In each part of the solution, we define
¿
to be where the breaks are first applied and
¡
to be where the system
(locomotive or locomotive and train cars) comes to a stop.
Dynamics 2e 683
Kinematic Equations.
The speed of the train in
¿
is
v1D120 km=hD1201000
3600 m=s
and in
¡
it is
v2D0. Since the train does not move vertically, the ycomponent of acceleration in Eq. (4) is ayD0.
684 Solutions Manual
Part (c).
Modeling the locomotive as a particle and the train of cars behind it as a
second particle, the FBD is as shown on the right, where
F
is the friction force between
Dynamics 2e 685
Problem 4.16
A classic car is driving down a 20
ı
incline at
45 km=h
when the
brakes are applied. Treat the car as a particle, and neglect all forces
except gravity and friction.
Using the work-energy principle, determine the stopping distance
if the tires slide and the coefficient of kinetic friction between the
tires and the road is 0:7.
Solution
686 Solutions Manual
Problem 4.17
A classic car is driving down a 20
ı
incline at
45 km=h
when the
brakes are applied. Treat the car as a particle, and neglect all forces
except gravity and friction.
Using the work-energy principle, determine the minimum stop-
ping distance if the car is retrofitted with antilock brakes and the tires
do not slide. Use
0:9
for the coefficient of static friction between the
tires and the road.
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.
