Vector Mechanics for Engineers: Statics and Dynamics
Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 2.1, Problem 2.4P

(a)

To determine

The magnitude (R) and direction (α) of the resultant force exerted on the bracket using the parallelogram law by graphical method.

(a)

Expert Solution
Check Mark

Answer to Problem 2.4P

The magnitude (R) and direction (α) of the resultant force exerted on the bracket is 8.03kips_ and 3.8°_ below the horizontal.

Explanation of Solution

Given information:

The tension (P) in the member B is 6 kips at an angle (θ) of 25° with the horizontal axis in clockwise direction.

The tension (Q) in the member C is 4 kips at an angle (ϕ) of 50° with the horizontal axis in the anticlockwise direction.

Calculation:

Calculate the angle (β) between the tension for Q and the vertical surface:

β=90°ϕ

Substitute 50° for ϕ.

β=90°50°=40°

Apply the parallelogram law for the force P and Q using the procedure as follows:

  • Draw the tension force P (6 kips) using the horizontal angle 25° from the origin point O with the coordinates (6cos25°,6sin25°).
  • Draw the tension force Q (4 kips) using the vertical angle 40° from the origin point O with the coordinates (4sin40°,4cos40°).
  • Draw a perpendicular line to the line OP from the force point P.
  • Draw a perpendicular line to the line OQ from the force point Q and make it intersect with the perpendicular line OP.
  • Draw a resultant force line by connecting the point O with the point S. Measure the angle α made by the horizontal axis with the resultant force line. It represents a parallelogram.
  • Measure the magnitude of resultant and angle α using the geometry from the parallelogram.

Sketch the parallelogram with the force P and Q as in Figure (1).

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.4P , additional homework tip  1

From Figure (1),

Measure the magnitude and the direction of the resultant force (R).

Thus, the magnitude (R) and direction (α) of the resultant force exerted on the bracket using the parallelogram law is 8.03kips_ and 3.8°_.

(b)

To determine

The magnitude (R) and direction (α) of the resultant force exerted on the bracket using the triangle rule by graphical method.

(b)

Expert Solution
Check Mark

Answer to Problem 2.4P

The magnitude (R) and direction (α) of the resultant force exerted on the bracket using the triangle law are 8.03kips_ and 3.8°_.

Explanation of Solution

Given information:

The tension (P) in the member B is 6 kips at an angle (θ) of 25° with the horizontal axis in clockwise direction.

The tension (Q) in the member C is 4 kips at an angle (ϕ) of 50° with the horizontal axis in the anticlockwise direction.

Calculation:

Apply the triangle law for the force P and Q using the procedure as follows:

  • Draw the tension force P (6 kips) using the horizontal angle 25° from the origin point O with the coordinates (6cos25°,6sin25°).
  • Draw the tension force Q (4 kips) using the horizontal angle 50° from the point P with the coordinates (4cos50°,4sin50°).
  • Draw a resultant force line by connecting the point O with the point Q. It is enclosed with triangle. The resultant force R makes an angle α with horizontal.
  • Measure the magnitude of resultant and angle α using the geometry from the triangle.

Sketch the triangle with the force P and Q as in Figure (2).

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.4P , additional homework tip  2

From Figure (2),

Measure the magnitude and the direction of the resultant force (R).

Thus, the magnitude (R) and direction (α) of the resultant force exerted on the bracket using the triangle law are 8.03kips_ and 3.8°_.

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Chapter 2 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - For the hook support of Prob. 2.10, determine by...Ch. 2.1 - Prob. 2.15PCh. 2.1 - Solve Prob. 2.1 by trigonometry.Ch. 2.1 - Solve Prob. 2.4 by trigonometry.Ch. 2.1 - For the stake of Prob. 2.5, knowing that the...Ch. 2.1 - 2.19 Two forces P and Q are applied to the lid of...Ch. 2.1 - 2.20 Two forces P and Q are applied to the lid of...Ch. 2.2 - Determine the x and y components of each of the...Ch. 2.2 - Determine the x and y components of each of die...Ch. 2.2 - Prob. 2.23PCh. 2.2 - Prob. 2.24PCh. 2.2 - Member BC exerts on member AC a force P directed...Ch. 2.2 - Member BD exerts on member ABC a force P directed...Ch. 2.2 - Prob. 2.27PCh. 2.2 - Cable AC exerts on beam AD a force P directed...Ch. 2.2 - The hydraulic cylinder BD exerts on member ABC a...Ch. 2.2 - The guy wire BD exerts on the telephone pole AC a...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Knowing that = 35, determine the resultant of the...Ch. 2.2 - 2.36 Knowing that the tension in rope AC is 365 N,...Ch. 2.2 - Knowing that = 40, determine the resultant of the...Ch. 2.2 - Knowing that = 75, determine the resultant of the...Ch. 2.2 - 2.39 For the collar of Prob. 2.35, determine (a)...Ch. 2.2 - Prob. 2.40PCh. 2.2 - PROBLEM 2.41 Determine (a) the required tension in...Ch. 2.2 - PROBLEM 2.42 For the block of Problems 2.37 and...Ch. 2.3 - Two cables are tied together at C and loaded as...Ch. 2.3 - Two forces of magnitude TA = 8 kips and TB = 15...Ch. 2.3 - The 60-lb collar A can slide on a frictionless...Ch. 2.3 - A chairlift has been stopped in the position...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Prob. 2.45PCh. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - 2 .47 Two cables are tied together at C and are...Ch. 2.3 - Knowing that = 20, determine the tension (a) in...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Prob. 2.51PCh. 2.3 - 2.52 Two forces P and Q arc applied as shown to an...Ch. 2.3 - A welded connection is in equilibrium under the...Ch. 2.3 - A welded connection is in equilibrium under the...Ch. 2.3 - A sailor is being rescued using a boatswains chair...Ch. 2.3 - A sailor is being rescued using a boatswains chair...Ch. 2.3 - For the cables of Prob. 2.44, find the value of ...Ch. 2.3 - For the cables of Prob. 2.46, it is known that the...Ch. 2.3 - For the situation described in Fig. P2.48,...Ch. 2.3 - 2 .60 Two cables tied together at C are loaded as...Ch. 2.3 - A movable bin and its contents have a combined...Ch. 2.3 - Prob. 2.62PCh. 2.3 - Collar A is connected as shown to a 50-lb load and...Ch. 2.3 - Collar A is connected as shown to a 50-lb load and...Ch. 2.3 - Prob. 2.65PCh. 2.3 - A 200-kg crate is to be supported by the...Ch. 2.3 - A 600-lb crate is supported by several...Ch. 2.3 - Solve parts b and d of Prob. 2.67, assuming that...Ch. 2.3 - A load Q is applied to the pulley C, which can...Ch. 2.3 - An 1800-N load Q is applied to pulley C, which can...Ch. 2.4 - 2.71 Determine (a) the x, y, and z components of...Ch. 2.4 - 2. 72 Determine (a) the x, y, and z components of...Ch. 2.4 - A gun is aimed at a point A located 35 east of...Ch. 2.4 - Solve Prob. 2.73 assuming that point A is located...Ch. 2.4 - Prob. 2.75PCh. 2.4 - Prob. 2.76PCh. 2.4 - Cable AB is 65 ft long, and the tension in that...Ch. 2.4 - PROBLEM 2.78 Cable AC is 70 ft long, and the...Ch. 2.4 - Prob. 2.79PCh. 2.4 - Prob. 2.80PCh. 2.4 - Prob. 2.81PCh. 2.4 - Prob. 2.82PCh. 2.4 - Prob. 2.83PCh. 2.4 - Prob. 2.84PCh. 2.4 - 2.85 A frame ABC is supported in part by cable DBE...Ch. 2.4 - Prob. 2.86PCh. 2.4 - In order to move a wrecked truck, two cables are...Ch. 2.4 - In order to move a wrecked truck, two cables are...Ch. 2.4 - A rectangular plate is supported by three cables...Ch. 2.4 - A rectangular plate is supported by three cables...Ch. 2.4 - Find the magnitude and direction of the resultant...Ch. 2.4 - Prob. 2.92PCh. 2.4 - Knowing that the tension is 425 lb in cable AB and...Ch. 2.4 - Knowing that the tension is 510 lb in cable AB and...Ch. 2.4 - Prob. 2.95PCh. 2.4 - Prob. 2.96PCh. 2.4 - The boom OA carries a load P and is supported by...Ch. 2.4 - Fig. P2.97 2.98 For the boom and loading of Prob....Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - A container of mass m = 120 kg is supported by...Ch. 2.5 - A 150-lb cylinder is supported by two cables AC...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - A container is supported by three cables that are...Ch. 2.5 - A container is supported by three cables that are...Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - Prob. 2.103PCh. 2.5 - Prob. 2.104PCh. 2.5 - Prob. 2.105PCh. 2.5 - Prob. 2.106PCh. 2.5 - Three cables are connected at A, where the forces...Ch. 2.5 - Fig. P2.107 and P2.108 2.108 Three cables are...Ch. 2.5 - Prob. 2.109PCh. 2.5 - A rectangular plate is supported by three cables...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - In trying to move across a slippery icy surface, a...Ch. 2.5 - Fig. P2.113 2.114 Solve Prob. 2.113 assuming that...Ch. 2.5 - For the rectangular plate of Probs. 2.109 and...Ch. 2.5 - PROBLEM 2.116 For the cable system of Problems...Ch. 2.5 - PROBLEM 2.117 For the cable system of Problems...Ch. 2.5 - Prob. 2.118PCh. 2.5 - For the transmission tower of Probs. 2.111 and...Ch. 2.5 - Three wires are connected at point D, which is...Ch. 2.5 - A container of weight W is suspended from ring A,...Ch. 2.5 - Prob. 2.122PCh. 2.5 - Prob. 2.123PCh. 2.5 - Prob. 2.124PCh. 2.5 - Fig. P2.113 2.114 Solve Prob. 2.113 assuming that...Ch. 2.5 - Prob. 2.126PCh. 2 - Prob. 2.127RPCh. 2 - Prob. 2.128RPCh. 2 - A hoist trolley is subjected to the three forces...Ch. 2 - Knowing that = 55 and that boom AC exerts on pin...Ch. 2 - Two cables are tied together at C and loaded as...Ch. 2 - Two cables tied together at C are loaded as shown....Ch. 2 - The end of the coaxial cable AE is attached to the...Ch. 2 - Prob. 2.134RPCh. 2 - Find the magnitude and direction of the resultant...Ch. 2 - Prob. 2.136RPCh. 2 - Collars A and B are connected by a 25-in.-lang...Ch. 2 - Fig. P2.137 and P2.138 2.138 Collars A and B are...
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