Explanation Given: The magnitude of component force, F 1 = 400 N The magnitude of component force, F 2 = 500 N The angle between F 2 and y axis is 60 ° . The angle between F 1 and z axis is 60 ° . The angle between F 2 and z axis is 135 ° . The angle between F 2 and x axis is 60 ° . Show the magnitude of component forces F 1 and F 2 as in Figure (1). Calculations: Calculate the magnitude of component vector force F 1 in Cartesian vector form. F 1 = F 1 ( sin 60 ° cos 20 ° i − sin 60 ° sin 20 ° j + cos 60 ° k ) N (I) Calculate the magnitude of component vector force F 2 in Cartesian vector form. F 2 = F 2 ( cos 60 ° i + cos 60 ° j + cos 135 ° k ) N (II) Calculate the magnitude of resultant vector force F R in Cartesian vector form. F R = F 1 + F 2 (III) Calculate the magnitude of resultant force F R . F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (IV) Calculate the coordinate direction angle α . cos α = ( F R ) x F R (V) Calculate the coordinate direction angle β . cos β = ( F R ) y F R (VI) Calculate the coordinate direction angle γ . cos γ = ( F R ) z F R (VII) Conclusion: Substitute 400 N for F 1 in Equation (I). F 1 = 400 ( sin 60 ° cos 20 ° i − sin 60 ° sin 20 ° j + cos 60 ° k ) N = 400 ( 0.8137 i − 0.296 j + 0.5 k ) N = { 325.5 i − 118.4 j + 200 k } N Substitute 500 N for F 2 in Equation (II). F 2 = 500 ( cos 60 ° i + cos 60 ° j + cos 135 ° k ) N = 500 ( 0.5 i + 0.5 j + ( − 0.7071 ) k ) N = { 250 i + 250 j − 353.55 k } N Substitute { 325.5 i − 118.4 j + 200 k } N for F 1 , and { 250 i + 250 j − 353

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2.6, Problem 77P

To determine

The magnitude and coordinate direction angles (α,β and γ) of resultant force and also sketch the obtained vector on the coordinate system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 76P

Chapter 2.6, Problem 78P

Students have asked these similar questions

The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth should be drawn near the pressure line so that the teeth from the pinion should mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or CAD drawing is acceptable. Draw all the trajectories of the involute lines and the circles. Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch. Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet, c=b-a.

5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces. The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2) is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2. (a) Find the revolution speed of gear 5. (b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue. (c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress). (d) According to the computation results of the questions (b) and (c), explain the possible failure mechanisms for each gear. N4=28 800rpm N₁=43 N5=34 N₂=14 P(diameteral pitch)=8 for all gears Coupled to 2.5hp motor

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 magnitude and coordinate direction angles ( α , β and γ ) of resultant force and also sketch the obtained vector on the coordinate system.

Solution Summary: The author calculates the magnitude of component vector force F_1 in Cartesian vector form.

Videos

The magnitude and coordinate direction angles (α,β and γ) of resultant force and also sketch the obtained vector on the coordinate system.

Want to see the full answer?

Chapter 2 Solutions