Midterm 1 - ENGG1210 - W23 - solutions

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School

University of Guelph *

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Course

1210

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Mechanical Engineering

Date

Apr 3, 2024

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docx

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Uploaded by PresidentBisonMaster300

: ENGINEERING MECHANICS Midterm Test 1: Instructions Instructor: Date: Friday February 3, 2023 Time: 6:00 pm Duration: 120 minutes for writing the exam. Student Name: _____________________________________________ Student Number: ____________________________________________ Instructions to Students 1. This is an in-person, invigilated exam. It is closed book, but students are allowed one 8.5” x 11” formula sheet, double-sided, hand-written. Any content may be included in the formula sheet. 2. By taking this exam, each student must agree to abide by the following code of conduct: a. the student's answers will be the student's own work; b. the student will not make answers available to anyone else. This includes both answers written by the student and any official answer keys provided by the course staff; c. the student will not engage in any other activities that will dishonestly improve the student's results or dishonestly improve-hurt the results of others; d. the student will behave honorably, appropriately, and with academic integrity. 3. For questions requiring a solution, you are required to show a detailed solution process. Marks are earned by demonstrating competency in solving a problem step-by-step. 4. The student is responsible for ensuring writing is legible. If the marker cannot read the answer, it will be automatically assumed incorrect. 5. To facilitate speedy marking, please underline final answers, or write in the box (where provided). Where applicable, units are required to earn full marks. 6. This test has 5 questions in total, each worth 10 marks, for a total of 50 marks. 7. This test contains 10 pages total. You may request additional pages, and please ensure these pages are securely tucked into the exam booklet when you submit at the end. 8. Please ensure that your name is written clearly at the top of each page. To ensure speedy marking, the staples will be removed, and exam sheets will be scanned. 9. For questions requiring a solution, they may be solved in different ways. We will only mark one attempt. Therefore, if you have solved a question in multiple ways, make sure you cross out the attempt you do not wish to be marked. 10. The instructors will not answer questions regarding the test. If you are unclear about a question, state any assumptions that you make and then write your answer clearly.

Name: ________________________ 11. Students arriving late will not be permitted extra time to complete the exam. 12. Students will not be permitted leave within the final 30 minutes of the writing time to avoid distracting others. Midterm 1. The four full-solution problems involve the application of Mechanics I concepts to a fictional visit to a dinosaur theme park. Numerical values at interfaces may have been simplified to make calculations easier. Bonus Predict your final grade on this test. If you are within ±10%, you will earn one bonus mark added to your final score. [1 mark] Prediction: ________ % Actual: /50 = % *Note: This is a metacognitive exercise for you to demonstrate you are aware of your own level of understanding of the material. This process can help you understand your strengths and weaknesses, and help you better prepare for future assessments. Question 1. Complete the following short-answer questions. Each is worth 2 marks , for a total of 10 marks . a. Draw the reaction forces / moments for the rod connected by a pin to the collar on a smooth rod (2D) on the coordinate system provided: *arrows can point in either direction for a. or b. 2

Name: ________________________ b. Draw the reaction forces / moments for the single smooth pin joint (3D) on the coordinate system provided: c. “We clocked the T-Rex being able to run at 32 miles per hour.” How fast is this in meters per second? A: 32 𝑚𝑖𝑙𝑒𝑠 𝑥 1 ℎ𝑜𝑢𝑟 𝑥 1609 𝑚𝑒𝑡𝑒𝑟𝑠 = 14.3 𝑚/𝑠 ℎ𝑜𝑢𝑟 3600 𝑠𝑒𝑐 1 𝑚𝑖𝑙𝑒 d. If ⃗𝐹⃗ 1 = {20 i + 50 j } N and ⃗𝐹⃗ 2 = {10 i – 10 j } N, determine the magnitude of the resultant force ( ⃗𝐹⃗ 1 + ⃗𝐹⃗ 2 ) in N. A: FR = 30 i = 50 N e. Determine the resultant moment produced about point A for the loading on the beam shown. A: Shortcut – recognize a couple moment. 50 sin 60 𝑁 × 2 𝑚 = + 𝟖𝟔. 𝟔 𝑵𝒎 Question 2. The bracket has three Compsognathus dinosaurs tethered to it using cables. The dinosaurs are pulling on it in different directions. Determine: a. The resultant force vector in pounds (lb) on the bracket. [6 marks] b. The magnitude of the resultant force in pounds (lb) on the bracket. [2 marks] 3

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Name: ________________________ c. The direction of the resultant force, measured clockwise from the positive x-axis. [2 marks] 4 Force vector: {89 i – 52 j } lb

Name: ________________________ Question 3. The instant when the Mosasaurus is pulling the food off the cable is modelled with simplification in the Cartesian coordinate system below. OA and DB are two vertical steel columns, each 20 feet tall to support the cable ACB. The food is hung by a pulley at point C and when it is being pulled, point C will lower to the coordinates (30, 40, 15) ft. When point C is being pulled, it will bear half of the weight of the 30,000 lb Mosasaurus, and the tension force on cable CA and CB are equal in magnitude. Use gravity = 32.2 ft/s 2 , assume the structure is in equilibrium, determine the following (keep two decimal places): a) Force vector ⃗𝑭⃗ 𝑪𝑨 ⃗ along cable CA in Cartesian form (units: lb); [3 marks] b) Force vector ⃗𝑭⃗ 𝑪𝑩 ⃗ along cable CB in Cartesian form (units: lb); [3 marks] c) The moment of ⃗𝑭⃗ 𝑪𝑨 ⃗ about the x-axis (vector form, units: ft•lb); [3 marks] d) The moment of ⃗𝑭⃗ 𝑪𝑩 ⃗ about column DB (magnitude only, units: ft•lb). [1 mark] 5 20 40 60 80 70 50 30 10 90 O A D B C W +z +y +x

Name: ________________________ 6 lb lb

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Name: ________________________ Question 4. The Greek philosopher Archimedes once said, “Give me a firm place to stand and a lever and I can move the Earth.” As being inspired by this quote, you want to ‘move’ a Ceratosaurus (520 kg). Assume the lever is sturdy (i.e. no deflections under load), with negligible thickness, partial dimensions of the lever are given in the diagram (BC = 4 m and CD = 2 m). The lever is in equilibrium while end D is touching the ground and the Ceratosaurus is standing at point C. Use g = 9.81 m/s 2 , keep one decimal place, determine: a) The moment about the pin joint at point B generated by the dinosaur at point C (units in kN•m); [2 marks] b) F D and F B (units in kN); [4 marks] c) The total length required for the entire lever (AD) to balance while a regular sized human (70 kg) stands at point A. Draw the FBD of the horizontally balanced lever scenario (human at point A, dinosaur at point C). [4 marks] 7

Name: ________________________ 8

Name: ________________________ Question 5. During feeding time, a 120 kg raptor jumps onto the tip of a cantilevered jib crane, while simultaneously the raptors in the pen pull on their lunch with a force of 10 kN. The crane is supported by a pin joint at A, and a rocker at B. Neglect the thickness and mass of the beams for all calculations. a. Determine the reaction forces and/or moments at the connection points A and B. [7 marks] b. The pins in the pin joint and rocker were ordered from the USA, and are specified to hold 3200 pounds (lbs) of force before failing. Which will fail? [3 marks] i. Pin A, Pin B, both, or neither? ii. If you don’t have a numerical value, you can also make a prediction and explain your rationale. 9

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