Explanation Establish a position vector from A to B . The coordinates of the points is A ( 5 c o s 40 ° , 8 , 5 s i n 40 ° ) ft and B ( 0 , 5 , 12 ) ft . Express the position vector r in the direction of AB . r A B = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (I) Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. Calculate the length of the chain. r A B = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (II) Express the force F as a Cartesian vector form and the position vector r is directed from point A to point B . F = F A B u A B = F A B ( r A B r A B ) = F A B ( r A B ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 ) (III) Here, the unit vector in the direction of AB is u A B , the position vector in the direction of AB is r A B , and the magnitude of the position vector in the direction of AB is r A B . Conclusion: Substitute 0 for x B , 5 ft for y B , 12 ft for z B , ( 5 cos 40 ° ) ft for x A , 8 ft for y A , and ( 5 sin 40 ° ) ft for z A in Equation (I). r A B = ( 0 − 5 cos 40 ° ) i + ( 5 − 8 ) j + ( 12 − 5 sin 40 ° ) k = ( 0 − 3.830 ) i + ( − 3 ) j + ( 12 − 3.214 ) k = { − 3.830 i − 3 j − 8.786 k } ft Substitute 0 for x B , 5 ft for y B , 12 ft for z B , ( 5 cos 40 ° ) ft for x A , 8 ft for y A , and ( 5 sin 40 ° ) ft for z A in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2.9, Problem 110P

To determine

The length of a chain, rAB.

The expression of vector force in Cartesian vector form.

The coordinate direction angles of the resultant force (α,β,γ).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.9, Problem 109P

Chapter 2.9, Problem 111P

Students have asked these similar questions

Q Derive (continuity equation)? I want to derive clear mathematics.

motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

First monthly exam Gas dynamics Third stage Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in 300 m length. Determine the flow rate in pipe. Use moody chart. Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe ( = 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 × 10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart (1) MIDAS Kel=0.3 Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e = 1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses. .μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³

Chapter 2 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Two forces act on the hook. Determine the...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - The force F = 450 lb acts on the frame. Resolve...Ch. 2.3 - If force F is to have a component along the u axis...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The length of a chain, r A B . The expression of vector force in Cartesian vector form. The coordinate direction angles of the resultant force ( α , β , γ ) .

Solution Summary: The author explains the expression of vector force in Cartesian vector form. The length of a chain is r_AB.

Videos

The length of a chain, rAB.

The expression of vector force in Cartesian vector form.

The coordinate direction angles of the resultant force (α,β,γ).

Want to see the full answer?

Chapter 2 Solutions

The length of a chain, r A B . The expression of vector force in Cartesian vector form. The coordinate direction angles of the resultant force ( α , β , γ ) .

Solution Summary: The author explains the expression of vector force in Cartesian vector form. The length of a chain is r_AB.

Videos

The length of a chain, rAB. The expression of vector force in Cartesian vector form. The coordinate direction angles of the resultant force (α,β,γ).

Want to see the full answer?

Chapter 2 Solutions

The length of a chain, rAB.

The expression of vector force in Cartesian vector form.

The coordinate direction angles of the resultant force (α,β,γ).