Chapter 8 Homework The weight of block E and the friction in the pulleys

CHAPTER 8

PROBLEM 8.1

Determine whether the block shown is in equilibrium and find the magnitude

and direction of the friction force whenP 150 N.

SOLUTION

Assume equilibrium:

PROBLEM 8.2

Determine whether the block shown is in equilibrium and find the magnitude

and direction of the friction force when P 400 N.

SOLUTION

Assume equilibrium:

PROBLEM 8.3

Determine whether the block shown is in equilibrium and find the

magnitude and direction of the friction force when P  120 lb.

SOLUTION

Assume equilibrium:

PROBLEM 8.4

Determine whether the block shown is in equilibrium and find the

magnitude and direction of the friction force when P  80 lb.

SOLUTION

Assume equilibrium:

PROBLEM 8.5

Determine the smallest value of P required to (a) start the block up the

incline, (b) keep it moving up.

SOLUTION

(a) To start block up the incline:

1

0.40

tan 0.40 21.80

s











PROBLEM 8.5 (Continued)

PROBLEM 8.6

The 20-lb block A hangs from a cable as shown. Pulley C is connected by a

short link to block E, which rests on a horizontal rail. Knowing that the

coefficient of static friction between block E and the rail is s = 0.35 and

neglecting the weight of block E and the friction in the pulleys, determine

the maximum allowable value of θ if the system is to remain in equilibrium.

SOLUTION

Free-body diagrams:

1

0.35

tan 0.35 19.29

s











PROBLEM 8.7

The 10-kg block is attached to link AB and rests on a moving belt.

Knowing that



s

= 0.30 and



k

= 0.25 and neglecting the weight of the

link, determine the magnitude of the horizontal force

P

that should be

applied to the belt to maintain its motion (a) to the left as shown, (b) to

the right.

SOLUTION

Link AB is a two-force member.

(a)

Free-body diagram of block:

Since there is motion between block and belt, use

1

0.25

tan 0.25 14.04

98.1 N

k

W













Free-body diagram of belt:

PROBLEM 8.7 (Continued)

(b) Free-body diagram of block:Free-body diagram of belt:

PROBLEM 8.8

Considering only values of



less than 90, determine the smallest value of



required to start the block moving to the right when (a) 75 lb,W



(b) 100 lb.W

SOLUTION

FBD block (Motion impending):

PROBLEM 8.9

Knowing that θ = 40°, determine the smallest force

P

for which equilibrium of the

7.5-kg block is maintained.

SOLUTION

Free-body diagram of block and force triangle:

Since we seek smallest P downward motion impends.



2

7.5 kg 9.81 m/s 73.575 NW

PROBLEM 8.10

Knowing that P = 100 N, determine the range of values of θ for which equilibrium

of the 7.5-kg block is maintained.

SOLUTION

Free-body diagram of block and force triangle:

For motion impending downward,



2

7.5 kg 9.81 m/s 73.575 NW

PROBLEM 8.10 (Continued)



100 N 73.575 N

sin

sin 114.23

s









PROBLEM 8.11

The 50-lb block A and the 25-lb block B are supported by an incline

that is held in the position shown. Knowing that the coefficient of

static friction is 0.15 between the two blocks and zero between block

B and the incline, determine the value of



for which motion is

impending.

SOLUTION

Since motion impends,

s

FN





between AB

Free body: Block A

PROBLEM 8.12

The 50-lb block A and the 25-lb block B are supported by an incline

that is held in the position shown. Knowing that the coefficient of

static friction is 0.15 between all surfaces of contact, determine the

value of



for which motion is impending.

SOLUTION

Since motion impends,

s

FN





between AB

Free body: Block A

PROBLEM 8.13

Three 4-kg packagesA, B, and C are placed on a conveyor belt that

is at rest. Between the belt and both packages A and C the

coefficients of friction are

0.30

s





and

0.20;

k





between

package B and the belt the coefficients are

0.10

s





and

0.08.

k





The packages are placed on the belt so that they are in contact with

each other and at rest. Determine which, if any, of the packages will

move and the friction force acting on each package.

SOLUTION

Consider C by itself: Assume equilibrium

0: cos15 0  

yC

FNW

cos 15 0.966

C

NW W

PROBLEM 8.13 (Continued)

Consider A and B together: Assume equilibrium

0.259

0.966

2(0.259 ) 0.518

AB

FF W

NN W

FF W W



 

PROBLEM 8.14

Solve Problem 8.13 assuming that package B is placed to the right of

both packages A and C.

PROBLEM 8.13

Three 4-kg packagesA, B, and C are placed on a

conveyor belt that is at rest. Between the belt and both packages A

and C the coefficients of friction are

0.30

s





and

0.20;

k





between package B and the belt the coefficients are

0.10

s





and

0.08.

k





The packages are placed on the belt so that they are in

contact with each other and at rest. Determine which, if any, of the

packages will move and the friction force acting on each package.

SOLUTION

Consider package B by itself: Assume equilibrium

0: cos15 0  

yB

FNW

cos 15 0.966

B

NW W

0: sin 15 0  

xB

FFW

sin 15 0.259

B

FW W

PROBLEM 8.14 (Continued)

Thus, ( ) ( ) ( ) 2(0.290 ) 0.0966

0.677

Am Cm Bm

FFF W W

W

 

