Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

Problems 627

Problems

18.1. The force – deflection relationships for three springs are

shown in the accompanying figure. What is the stiff-

ness (spring constant) of each spring? Which one of

the springs is the stiffest?

18.3. The equations describing the position of a water stream

(with respect to time) coming out of the hose, shown in

the accompanying figure, are given by

In these relationships,xandyare position coordinates,

x 0 andy 0 are initial coordinates of the tip of the hose,

(vx) 0 and (vy) 0 are the initial velocities of water coming

out of the hose in thexandydirections,g9.81 m/s

2

,

andtis time.

Plot thexand theyposition of the water stream as

a function of time. Also, plot the path the water stream

will follow as a function of time. Compute and plot

the components of velocity of the water stream as a

function of time.

yy 0  1 vy 20 t

1

2

gt

2

xx 0  1 vx 20 t

Spring Force (N)

40

30

20

10

0

0246810

Deflection (mm)

Spring A

Spring B

Spring C

Problem 18.1

Spring Force (N)

40

30

20

10

0

0246810

Deflection (mm)

Spring A

Spring B

Problem 18.2

18.2. In the accompanying diagram, spring A is a linear

spring and spring B is a hard spring, with characteristics

that are described by the relationshipFkx

n

. Deter-
mine the stiffness coefficientkfor each spring. What
is the exponentnfor the hard spring? In your own
words, also explain the relationship between the spring
force and the deflection for the hard spring and how it
differs from the behavior of the linear spring.

(Vx) 0  2.6 m/s

(Vy) 0  1.5 m/s

x 0  2m

Hose

x

y

V

y 0  1.5 m

Problem 18.3

18.4. In Chapter 12, we explained that the electric power

consumption of various electrical components can be

determined using the following power formula:P

VIRI

2

; wherePis power in Watts,Vis the voltage,

Iis the current in amps, andRis the resistance of the

component in ohms.

Plot the power consumption of an electrical com-

ponent with a resistance of 145 ohms. Vary the value

of the current from zero to 4 amps. Discuss and plot

the change in power consumption as the function of

current drawn through the component.

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀