Express the force f in cartesian vector form if it acts at the midpoint b of the rod.

MAE 201 – Mechanics of Particles and Rigid Bodies I: Statics – Fall 2017

1

Assignment: #1 Total Problems 60 points total. Each problem is worth 10 points

Due: 4:00 PM, September 2nd, 2017 Instructions: Complete all of the assigned problems. You do not need to

complete and submit the suggested problems. Suggested problems will be uploaded in a separate document on piazza.

All solutions must follow the seven-step problem setup process detailed in class. Failure to follow this process will result in a 0 for that problem. Remember that only variables are allowed in your schematics or FBDs – no numbers. Write N/A if a step does not apply to a particular problem (example, there may not be any assumptions if you are just computing the angle between two vectors, so Step 5 could read: 5) Assumptions: N/A).

Problem: 1. A weight 𝑊 of 100 𝑙𝑏𝑓 is supported by a system of wires as shown below. Find the tension 𝑇! , 𝑇! , 𝑇! , and 𝑇! in the wires of the system.

Suggested Review Problems: S1-1 through S1-5

Problem: 2. The two vectors 𝑎 and 𝑏 in the figure shown below have equal magnitudes of 10.0 𝑚. Find:

a. Their vector sum 𝑟 using the parallelogram law. b. The 𝑥 and 𝑦 components of their vector sum 𝑟. c. The magnitude of their vector sum 𝑟. d. The angle 𝑟 makes with the positive direction of the 𝑥 axis.

Suggested Review Problems: S2-1 through S2-5

127

© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–106.

Express the force F in Cartesian vector form if it acts at the midpoint B of the rod.

SOLUTION

rAB = rAC 2

= -3i + 4j - 4k

2 = -1.5i + 2j - 2k

rAD = rAB + rBD rBD = rAD - rAB

= (4i + 6j - 4k) - (-1.5i + 2j - 2k)

= {5.5i + 4j - 2k} m

rBD = 2(5.5)2 + (4)2 + (-2)2 = 7.0887 m F = 600 arBD

rBD b = 465.528i + 338.5659j - 169.2829k

F = {466i + 339j - 169k} N Ans.

3 m

4 m y

x

z

6 m

4 m

4 m

O F ! 600 N

B

A

C

D

Ans: F = {466i + 339j - 169k} N

x

u⃗

q⃗

A(0, 0, 6) B lies along line AC C(-3, 4, 0) D(4, 5, 0)

Problem: 3. Compute the total force exerted by the four forces exerted on the eye hook. Express the solution in terms of the magnitude and direction (clockwise rotation from the x-axis) of the resultant force. Suggested Review Problems: S3-1 through S3-3

Problem: 4. In the schematic below, point B lies a distance x from point A along line AC; u is the unit vector along line AC, and q is the unit vector along line BD. The locations for A, C, D are listed in the schematic. In Cartesian coordinates/vector form: i) find the unit vector u; ii) find the coordinates for point B as a function of x. iii) Find the unit vector q as a function of x. Suggested Review Problems: S4-1 through S4-6

Problem: 5. (a) Determine the magnitude of the resultant force acting on the eyebolt; (b) determine the coordinate direction angle α of the resultant force acting on the eyebolt; (c) determine the coordinate direction angle β of the resultant force. Suggested Review Problems: S5_6-1 through S5_6-3

Problem: 6. Determine the magnitude and coordinate direction angles of F3 so that the resultant of the three forces is zero. NOTE: figure not drawn to scale. Suggested Review Problems: S5_6-1 through S5_6-3 (same as for Problem 5)

Applied Sciences

Architecture and Design

Biology

Business & Finance

Chemistry

Computer Science

Geography

Geology

Education

Engineering

English

Environmental science

Spanish

Government

History

Human Resource Management

Information Systems

Law

Literature

Mathematics

Nursing

Physics

Political Science

Psychology

Reading

Science

Social Science

Home

Blog

Archive

Contact

google+twitterfacebook

Copyright © 2019 HomeworkMarket.com