978-0073380308 Chapter 4 Solution Manual Part 2

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

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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.