Explanation Given: The magnitude of the component vector force F 1 , F 1 = 600 N . The magnitude of the component vector force F 2 , F 2 = 450 N . Angle between F ′ and x -axis is 30 ° . Angle between F 2 and y axis is 45 ° . Show the magnitude of the components forces F 1 and F 2 in x , y , and z directions as in Figure (1). Show the direction angles with magnitude of component forces F 1 and F 2 as in Figure (2). Write the vector force F 1 in Cartesian vector form using Figure 1. F 1 = ( F 1 ) x i + ( F 1 ) y ( − j ) + ( F 1 ) z ( + k ) = ( F ′ cos 30 ° ) i + ( F ′ sin 30 ° ) ( − j ) + ( F 1 sin θ ) ( + k ) = ( F 1 cos θ cos 30 ° ) i − ( F 1 cos θ sin 30 ° ) j + ( F 1 sin θ ) k (I) Here, the unit vectors are i , j , and k , and the sum of forces F x and F y is F ′ . Write the vector force F 2 in Cartesian vector form using Figure 2. F 2 = ( F 2 ) x i + ( F 2 ) y ( + j ) + ( F 2 ) z ( + k ) = 0 i + ( F 2 cos 45 ° ) ( + j ) + ( F 2 sin 45 ° ) ( + k ) (II) Here, the component force F 2 in x , y , and z axes are F 2 x , F 2 y , and F 2 z , respectively. Express the resultant force of vector force F 1 and F 2 . F R = F 1 + F 2 (III) Write the magnitude of the resultant force. F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (IV) Here, the magnitude of the resultant force measured along x , y , and z axes is ( F R ) x , ( F R ) y , and ( F R ) z . Determine the coordinate direction angles. cos α = ( F R ) x F R (V) cos β = ( F R ) y F R (VI) cos γ = ( F R ) z F R (VII) Conclusion: Substitute 600 N for F 1 , 3 / 5 for sin θ , and 4 / 5 for cos θ in Equation (I)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 2.6, Problem 76P

To determine

The magnitude (FR) and coordinate direction angles of the resultant force acting on the eyebolt (α,β, and γ).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 75P

Chapter 2.6, Problem 77P

Students have asked these similar questions

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

2/Y Y+1 2Cp Q1/ Show that Cda Az x P1 mactual Cdf Af R/T₁ 2pf(P1-P2-zxgxpf) Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec. Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible. Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The temperature of air decreases with altitude as given by the expression The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State any assumptions made. t = ts P 0.0065h

36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

Chapter 2 Solutions

Engineering Mechanics: Statics

Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....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 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...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...Ch. 2.3 - Determine the magnitude of the resultant force FR...

Knowledge Booster

The magnitude ( F R ) and coordinate direction angles of the resultant force acting on the eyebolt ( α , β , and γ ) .

The magnitude (FR) and coordinate direction angles of the resultant force acting on the eyebolt (α,β, and γ).

Want to see the full answer?

Chapter 2 Solutions