978-0077687342 Chapter 16 Part 1

CHAPTER 16

PROBLEM 16.1

A 60–lb uniform thin panel is placed in a truck with end A resting

on a rough horizontal surface and end B supported by a smooth

vertical surface. Knowing that the deceleration of the truck is 12

2

ft/s ,

determine (a) the reactions at ends A and B, (b) the

minimum required coefficient of static friction at end A.

PROBLEM 16.2

A 60-lb uniform thin panel is placed in a truck with end A resting

on a rough horizontal surface and end B supported by a smooth

vertical surface. Knowing that the panel remains in the position

shown, determine (a) the maximum allowable acceleration of the

truck, (b) the corresponding minimum required coefficient of

static friction at end A.

PROBLEM 16.3

Knowing that the coefficient of static friction between the tires

and the road is 0.80 for the automobile shown, determine the

maximum possible acceleration on a level road, assuming (a) four–

wheel drive, (b) rear–wheel drive, (c) front–wheel drive.

SOLUTION

(a) Four-wheel drive:

0.84

PROBLEM 16.3 (Continued)

(c) Front-wheel drive:

1.16

PROBLEM 16.4

The motion of the 2.5-kg rod AB is guided by two small wheels which roll

freely in horizontal slots. If a force P of magnitude 8 N is applied at B,

determine (a) the acceleration of the rod, (b) the reactions at A and B.

PROBLEM 16.5

A uniform rod BC of mass 4 kg is connected to a collar A by a 250-mm

cord AB. Neglecting the mass of the collar and cord, determine (a) the

smallest constant acceleration

A

a

for which the cord and the rod lie in a

straight line, (b) the corresponding tension in the cord.

cos cos 22.62

θ

PROBLEM 16.6

A 2000-kg truck is being used to

lift a 400–kg boulder B that is on a

50–kg pallet A. Knowing the

acceleration of the rear–wheel drive

truck is 1 m/s2, determine (a) the

reaction at each of the front

wheels, (b) the force between the

boulder and the pallet.

SOLUTION

2

PROBLEM 16.6 (Continued)

PROBLEM 16.7

The support bracket shown is used to transport a cylindrical can from one

elevation to another. Knowing that

0.25

s

µ

=

between the can and the

bracket, determine (a) the magnitude of the upward acceleration a for which

the can will slide on the bracket, (b) the smallest ratio h/d for which the can

will tip before it slides.

SOLUTION

Nh

d=

PROBLEM 16.8

Solve Problem 16.7, assuming that the acceleration a of the bracket is directed

downward.

PROBLEM 16.7 The support bracket shown is used to transport a

cylindrical can from one elevation to another. Knowing that

0.25

s

µ

=

between the can and the bracket, determine (a) the magnitude of the upward

acceleration a for which the can will slide on the bracket, (b) the smallest

ratio h/d for which the can will tip before it slides.

SOLUTION

Nh

d=

PROBLEM 16.9

A 20–kg cabinet is mounted on casters that allow it to move freely

( 0)

µ

=

on the floor. If a 100-N force is applied as shown, determine

(a) the acceleration of the cabinet, (b) the range of values of h for which

the cabinet will not tip.

SOLUTION

PROBLEM 16.10

Solve Problem 16.9, assuming that the casters are locked and slide on

the rough floor

( 0.25).

k

µ

=

PROBLEM 16.9 A 20-kg cabinet is mounted on casters that allow it to

move freely

( 0)

µ

=

on the floor. If a 100-N force is applied as shown,

determine (a) the acceleration of the cabinet, (b) the range of values of

h for which the cabinet will not tip.

SOLUTION

1.047 m

h

=

PROBLEM 16.10 (Continued)

PROBLEM 16.11

A completely filled barrel and its contents have a combined

mass of 90 kg. A cylinder C is connected to the barrel at a

height h = 550 mm as shown. Knowing

0.40

s

µ

=

and

0.35,

k

µ

=

determine the maximum mass of C so the barrel

will not tip.

SOLUTION

90 90

PROBLEM 16.11 (Continued)

PROBLEM 16.12

A 40-kg vase has a 200-mm–diameter base and is being

moved using a 100–kg utility cart as shown. The cart

moves freely (

µ

= 0) on the ground. Knowing the

coefficient of static friction between the vase and the

cart is

µ

s = 0.4, determine the maximum force F that can

be applied if the vase is not to slide or tip.

PROBLEM 16.12 (Continued)

Cart and vase:

PROBLEM 16.13

The retractable shelf shown is supported

by two identical linkage–and–spring

systems; only one of the systems is

shown. A 20-kg machine is placed on the

shelf so that half of its weight is supported

by the system shown. If the springs are

removed and the system is released from

rest, determine (a) the acceleration of the

machine, (b) the tension in link AB.

Neglect the weight of the shelf and links.

SOLUTION

0.11928 0.150 0.04990 cos30

A

F mg mg

−=− °