Mechanical Engineering Chapter 17 Homework Determine how far the door moves in 2 s

811

17–21.

SOLUTION

G

2m

y

O

T

he

pendulum

consists

of

the

3-kg

slender

rod

and

the

5-kg thin plate. Determine the location y of the center of

mass G

of

the

pendulum;

then

calculate

the

moment

of

inertia

of

the

pendulum

about

an

axis

perpendicular

to

the

page and passing through G.

812

17–22.

90 mm

50 mm

20 mm

x

x¿

30 mm

180 mm

Determine the moment of inertia of the overhung crank

about the xaxis.The material is steel having a destiny of

.r=7.85 Mg>m3

SOLUTION

mc=7.85(103)

A

(0.05)p(0.01)2

B

=0.1233 kg

Ans:

17–23.

90 mm

50 mm

20 mm

x

x¿

30 mm

180 mm

Determine the moment of inertia of the overhung crank

about the axis.The material is steel having a destiny of

r=7.85 Mg>m3.

x¿

SOLUTION

mc=7.85

A

103

BA

(0.05)p(0.01)2

B

=0.1233 kg

814

*17–24.

SOLUTION

:

+©Fx=m(aG)x;30=(200

32.2)aG

The door has a weight of 200 lb and a center of gravity at G.

Determine how far the door moves in 2 s, starting from rest,

if a man pushes on it at Cwith a horizontal force

Also, find the vertical reactions at the rollers Aand B.

F=30 lb.

6ft6ft

AB

CG12 ft

5ft

3ft

F

Ans:

815

17–25.

The door has a weight of 200 lb and a center of gravity at G.

Determine the constant force Fthat must be applied to the

door to push it open 12 ft to the right in 5 s, starting from

rest. Also, find the vertical reactions at the rollers Aand B.

SOLUTION

(:

+)s=s0+

v

0t+1

2aGt2

6ft6ft

AB

CG12 ft

5ft

3ft

F

Ans:

816

17–26.

The jet aircraft has a total mass of 22 Mg and a center of

mass at G. Initially at take-off the engines provide a thrust

and Determine the acceleration of

the plane and the normal reactions on the nose wheel and

each of the two wing wheels located at B. Neglect the mass

of the wheels and, due to low velocity, neglect any lift

caused by the wings.

T¿=1.5 kN.2T=4kN

SOLUTION

T¿2TG

2.5m 2.3m B

1.2m

A

6m3m

Ans:

817

17–27.

SOLUTION

The sports car has a weight of 4500 lb and center of gravity

at G. If it starts from rest it causes the rear wheels to slip

as it accelerates. Determine how long it takes for it to reach

a speed of 10 ft/s. Also, what are the normal reactions at

each of the four wheels on the road? The coefficients of

static and kinetic friction at the road are and

respectively. Neglect the mass of the wheels.mk=0.3,

ms=0.5 4ftAB

G

2ft

2.5 ft

Ans:

818

*17–28.

The assembly has a mass of 8 Mg and is hoisted using the

boom and pulley system. If the winch at B draws in the cable

with an acceleration of 2 m

>

s2, determine the compressive

force in the hydraulic cylinder needed to support the boom.

The boom has a mass of 2 Mg and mass center at G.

G

C

aB=–2aL

4 m

2 m

6 m

B60

SOLUTION

sB+2sL=l

Ans:

819

17–29.

The assembly has a mass of 4 Mg and is hoisted using the

winch at B. Determine the greatest acceleration of the

assembly so that the compressive force in the hydraulic

cylinder supporting the boom does not exceed 180 kN. What

is the tension in the supporting cable? The boom has a mass

of 2 Mg and mass center at G.

Ans:

G

C

4 m

2 m

6 m

B60

SOLUTION

820

17–30.

The uniform girder AB has a mass of 8 Mg. Determine the

internal axial, shear, and bending-moment loadings at the

center of the girder if a crane gives it an upward acceleration

of 3 m

>

s2.

Ans:

SOLUTION

Girder:

Segment:

S

+Σ

F

ma

59 166.86 cos 60°–N=0

C

3 m/s2

821

17–31.

A car having a weight of 4000 lb begins to skid and turn with

the brakes applied to all four wheels. If the coefficient of

kinetic friction between the wheels and the road is m

k=0.8,

determine the maximum critical height h of the center of

gravity G such that the car does not overturn. Tipping will

begin to occur after the car rotates 90° from its original

direction of motion and, as shown in the figure, undergoes

translation while skidding. Hint: Draw a free-body diagram

of the car viewed from the front. When tipping occurs, the

normal reactions of the wheels on the right side (or passenger

side) are zero.

Ans:

SOLUTION

NA

represents the reaction for both the front and rear wheels on the left side.

y

x

2.5 ft

2.5 ft h

z

G

822

*17–32.

A force of

P=300 N

is applied to the 60-kg cart. Determine

the reactions at both the wheels at A and both the wheels

at B. Also, what is the acceleration of the cart? The mass

center of the cart is at G.

0.3 m

0.2 m

0.3 m

0.4 m

30

AB

G

P

SOLUTION

Equations of Motions. Referring to the FBD of the cart, Fig. a,

Solving Eqs. (1) and (2),

Ans:

823

17–33.

Determine the largest force P that can be applied to the

60-kg cart, without causing one of the wheel reactions,

either at A or at B, to be zero. Also, what is the acceleration

of the cart? The mass center of the cart is at G.

Ans:

SOLUTION

Equations of Motions. Since

(0.38 m) tan 30°=0.22 m 70.1 m

, the line of action

0.3 m

0.2 m

0.3 m

0.4 m

30

AB

G

P

824

17–34.

SOLUTION

Equations of Motion: Writing the force equation of motion along the xaxis,

Using this result to write the force equation of motion along the yaxis,

A=326.81 N =327 N

The trailer with its load has a mass of 150 kg and a center of

mass at G. If it is subjected to a horizontal force of

, determine the trailer’s acceleration and the

normal force on the pair of wheels at Aand at B.The

wheels are free to roll and have negligible mass.

P=600 N

1.25 m

0.75 m 1.25 m

0.25 m

0.25 m 0.5 m

G

BA

P600

N

Ans:

825

17–35.

The desk has a weight of 75 lb and a center of gravity at G.

Determine its initial acceleration if a man pushes on it with

a force

F=60 lb.

The coefficient of kinetic friction at A

and B is m

k=0.2.

Ans:

SOLUTION

G

F

A

30

B

1 ft

2 ft

826

*17–36.

The desk has a weight of 75 lb and a center of gravity at G.

Determine the initial acceleration of a desk when the man

applies enough force F to overcome the static friction at A

and B. Also, find the vertical reactions on each of the

two legs at A and at B. The coefficients of static and kinetic

friction at A and B are m

s=0.5

and m

k=0.2,

respectively.

G

F

A

30

B

2 ft 2 ft

1 ft

2 ft

SOLUTION

Force required to start desk moving;

NA+NB–F sin 30°–75 =0

Solving for F by eliminating

NA+NB

,

Desk starts to slide.

NA+NB–60.874 sin 30°–75 =0

NA+NB

So that

Ans:

827

17–37.

The 150-kg uniform crate rests on the 10-kg cart. Determine

the maximum force P that can be applied to the handle

without causing the crate to tip on the cart. Slipping does

not occur.

1 m

0.5 m

P

SOLUTION

Equation of Motion. Tipping will occur about edge A. Referring to the FBD and

kinetic diagram of the crate, Fig. a,

Using the result of a and refer to the FBD of the crate and cart, Fig. b,

828

17–38.

The 150-kg uniform crate rests on the 10-kg cart. Determine

the maximum force P that can be applied to the handle

without causing the crate to slip or tip on the cart. The

coefficient of static friction between the crate and cart is

m

s=0.2.

Ans:

1 m

0.5 m

P

SOLUTION

Equation of Motion. Assuming that the crate slips before it tips, then

F

f

=

ms

N=0.2 N.

Referring to the FBD and kinetic diagram of the crate, Fig. a

Since

x=0.1 m 60.25 m

, the crate indeed slips before it tips. Using the result of a

829

17–39.

The bar has a weight per length w and is supported by the

smooth collar. If it is released from rest, determine the

internal normal force, shear force, and bending moment in

the bar as a function of x.

Ans:

30

x

SOLUTION

Entire bar:

830

*17–40.

The smooth 180-lb pipe has a length of 20 ft and a negligible

diameter. It is carried on a truck as shown. Determine the

maximum acceleration which the truck can have without

causing the normal reaction at A to be zero. Also determine

the horizontal and vertical components of force which the

truck exerts on the pipe at B.

SOLUTION

B

A

20 ft

5 ft

Ans: