Chapter 2 Homework Two forces are applied as shown to a hook

CHAPTER 2

PROBLEM 2.1

Two forces are applied as shown to a hook. Determine graphically the

magnitude and direction of their resultant using (a) the parallelogram law,

(b) the triangle rule.

SOLUTION

(a) Parallelogram law:

PROBLEM 2.2

Two forces are applied as shown to a bracket support. Determine

graphically the magnitude and direction of their resultant using

(a) the parallelogram law, (b) the triangle rule.

SOLUTION

(a) Parallelogram law:

PROBLEM 2.3

Two structural members B and C are bolted to bracket A. Knowing that

both members are in tension and that P = 10 kN and Q = 15 kN,

determine graphically the magnitude and direction of the resultant force

exerted on the bracket using (a) the parallelogram law, (b) the triangle

rule.

SOLUTION

(a) Parallelogram law:

PROBLEM 2.4

Two structural members B and C are bolted to bracket A. Knowing that

both members are in tension and that P = 6 kips and Q = 4 kips,

determine graphically the magnitude and direction of the resultant force

exerted on the bracket using (a) the parallelogram law, (b) the triangle

rule.

SOLUTION

(a) Parallelogram law:

PROBLEM 2.5

A stake is being pulled out of the ground by means of two ropes as shown.

Knowing that α = 30°, determine by trigonometry (a) the magnitude of the

force P so that the resultant force exerted on the stake is vertical, (b) the

corresponding magnitude of the resultant.

SOLUTION

PROBLEM 2.6

A telephone cable is clamped at A to the pole AB. Knowing that the

tension in the left–hand portion of the cable is T1 = 800 lb, determine

by trigonometry (a) the required tension T2 in the right-hand portion if

the resultant R of the forces exerted by the cable at A is to be vertical,

(b) the corresponding magnitude of R.

SOLUTION

PROBLEM 2.7

A telephone cable is clamped at A to the pole AB. Knowing that the

tension in the right-hand portion of the cable is T2 = 1000 lb, determine

by trigonometry (a) the required tension T1 in the left–hand portion if

the resultant R of the forces exerted by the cable at A is to be vertical,

(b) the corresponding magnitude of R.

SOLUTION

PROBLEM 2.8

A disabled automobile is pulled by means of two

ropes as shown. The tension in rope AB is 2.2 kN,

and the angle α is 25°. Knowing that the resultant

of the two forces applied at A is directed along the

axis of the automobile, determine by trigonometry

(a) the tension in rope AC, (b) the magnitude of the

resultant of the two forces applied at A.

SOLUTION

PROBLEM 2.9

A disabled automobile is pulled by means of two

ropes as shown. Knowing that the tension in rope

AB is 3 kN, determine by trigonometry the tension

in rope AC and the value of α so that the resultant

force exerted at A is a 4.8–kN force directed along

the axis of the automobile.

SOLUTION

PROBLEM 2.10

Two forces are applied as shown to a hook support. Knowing that the

magnitude of P is 35 N, determine by trigonometry (a) the required

angle

α

if the resultant R of the two forces applied to the support is to

be horizontal, (b) the corresponding magnitude of R.

SOLUTION

Using the triangle rule and law of sines:

(a)

PROBLEM 2.11

A steel tank is to be positioned in an excavation. Knowing

that

α

= 20°, determine by trigonometry (a) the required

magnitude of the force P if the resultant R of the two

forces applied at A is to be vertical, (b) the corresponding

magnitude of R.

SOLUTION

PROBLEM 2.12

A steel tank is to be positioned in an excavation. Knowing

that the magnitude of P is 500 lb, determine by

trigonometry (a) the required angle

α

if the resultant R of

the two forces applied at A is to be vertical, (b) the

corresponding magnitude of R.

SOLUTION

PROBLEM 2.13

A steel tank is to be positioned in an excavation.

Determine by trigonometry (a) the magnitude and

direction of the smallest force P for which the resultant R

of the two forces applied at A is vertical, (b) the

corresponding magnitude of R.

SOLUTION

PROBLEM 2.14

For the hook support of Prob. 2.10, determine by trigonometry (a) the

magnitude and direction of the smallest force P for which the resultant

R of the two forces applied to the support is horizontal, (b) the

corresponding magnitude of R.

SOLUTION

PROBLEM 2.15

For the hook support shown, determine by trigonometry the

magnitude and direction of the resultant of the two forces applied

to the support.

SOLUTION

PROBLEM 2.16

Solve Prob. 2.1 by trigonometry.

PROBLEM 2.1

Two forces are applied as shown to a hook. Determine graphically the

magnitude and direction of their resultant using (a) the parallelogram law,

(b) the triangle rule.

SOLUTION

PROBLEM 2.17

Solve Problem 2.4 by trigonometry.

PROBLEM 2.4 Two structural members B and C are bolted to bracket

A. Knowing that both members are in tension and that P = 6 kips and

Q = 4 kips, determine graphically the magnitude and direction of the

resultant force exerted on the bracket using (a) the parallelogram law,

(b) the triangle rule.

SOLUTION

Using the force triangle and the laws of cosines and sines:

We have:

180 (50 25 )

105

γ

= °− °+ °

= °

PROBLEM 2.18

For the stake of Prob. 2.5, knowing that the tension in one rope is 120 N,

determine by trigonometry the magnitude and direction of the force P so

that the resultant is a vertical force of 160 N.

PROBLEM 2.5 A stake is being pulled out of the ground by means of two

ropes as shown. Knowing that α = 30°, determine by trigonometry (a) the

magnitude of the force P so that the resultant force exerted on the stake is

vertical, (b) the corresponding magnitude of the resultant.

SOLUTION