Name ME 270 Fall 2005 Final Exam PROBLEM NO. 1 Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Find: a) Draw a free body diagram of link BCDE and one of link AC. (7 points) b) List any two force members. (2 points) c) Determine the forces at points A, D, and E. (11 points)
Name ME 270 Fall 2005 Final Exam PROBLEM NO. 2 Statics short answer. Each part of this problem is worth 5 points. Please answer them as succinctly as possible. 2A. If the tensile force in cable CD is 750 N, calculate the moment exerted by the force in the cable about point A. (5 points)
Name 2C. Calculate the y-component of the centroid for the simulated B2 bomber wing. (5 points)
Last Name, First Name 2. The device shown below is used to crush cans. The user places the can at point C (the arrow represents the force that the can exerts on the device) and presses down on the handle with a force, P. The force, C, to crush a can is ten pounds when the angle θ = 36.87º. Assume that there is NO Friction on the collar for link BC. 2a. Circle all of the links listed below that are two-force members (3 points) BC AB OP 2b. Draw a free body diagram of link OP (3 points)
Last Name, First Name 2c. Draw a free body diagram of link AB (3 points) 2d. Draw a free body diagram of link BC (3 points)
Last Name, First Name 2e. Determine the force, P, required to crush a can (4 points) 2f. Determine the reactions at O (4 points)
Last Name, First Name 4a. Here is an odd-looking beam assembly. Sometimes these kind of contraptions are used in fail-safe devices. That is, they are designed to fail when a certain load is applied. The beam AC weighs 25 lbs. and beam CD weighs 20 lbs. Draw a free body diagram of link AC and determine the force at point C. (5 points) Draw a free body diagram of link CD and determine the force at point D. (4 points)
Name ME 270 Fall 2007 Final Exam PROBLEM NO. 1 (25 points) Short Answer 1A. Please state Newton s three laws as succinctly as possible in order. (5 points) Newton s 1 st Law: Newton s 2 nd Law: Newton s 3 rd Law: 1B. Please fill in the table below. How many scalar equations can be generated for a free body diagram of a particle or a rigid body in two dimensions and three dimensions in static equilibrium. (5 points) 2D 3D Particle Rigid Body
Name 1E. A massless wedge is used to move Block B (which weighs 500 lb.) to the right by applying force P. Frictionless rollers are located between the wedge and Block B. Which is the correct free-body diagram: Figure a, Figure b or Figure c? Circle the correct answer and record it in the space provided above. (5 points) P Figure a F w N 1 W Block B 500 lb y N w N 1 75 x F b N b P. Figure b y N w F w N 1 F i W N 1 F i x F b N b P Figure c y N w F w N 1 W N 1 x F b N b
Name ME 270 Fall 2007 Final Exam PROBLEM NO. 3 (25 points) Given: A triangular-shaped concrete block is connected to a pin joint at O. The specific weight of the concrete is γ = ρg = 150 lb/ft 3. The specific weight of the water is 62.4 lb/ft 3. The height of the water is at 9 feet (top of the block). The depth (distance out of the paper is 5.00 feet) for the water and the concrete block. There is no friction between the concrete and the ground beneath. A moment, M, is applied to prevent tipping. Find: Determine the weight of the concrete block and its center of mass (4 points). Determine the resultant force and point of application for the water (4 points). Draw a free-body diagram of the concrete block at the instant of impending tipping and specify all loads. (6 points) Determine the minimum moment required so that the concrete block will not tip (8 points all work must be shown) Determine the horizontal force at point O (3 points)
Problem 2 ME 270 Fall 2008 Name Part i. By inspection, determine all the zero-force members in the truss below and list them in the box provided (5 points) Zero-force members: Part ii. A 50-lb block with a thickness of 1-ft out of the page is used retain water. The block will not slide. A force P is used to prevent the block from tipping over. The height of water h = 4 ft. a. Please determine the center of mass (x c and y c ) for the block relative to block O. The block is 3-ft wide and 5-ft tall (4 points) b. If the specific weight of the water is given as γ=62.4 lb/ft 3 please determine the force P to prevent tipping about point O (6 points) ii a. x c = y c = ft. ft. y ii b. h= ft. 5-ft h O 3-ft x
Problem 8-Practice Final ME 270 Fall 2008 Name A distributed load is also applied to the beam below, determine: a. The magnitude of the distributed load and the point of application (8 points). c. The reactions at the wall of the beam (7 points).
Name (Last)(First) 2a.Byinspection,determineallthezero forcemembersinthetrussbelowandlisttheminthebox provided(4points) Zero forcemembers: 2b.A60 lbtriangularblockwithathicknessof1 ftoutofthepageisusedretainwater.theblock willnotslide. a. Pleasedeterminethecenterofmass(x candy c)forthetriangularblockrelativetopointo. Theblockis3 ftwideand5 fttall(4points) b. Ifthespecificweightofthewaterisgivenasγ=62.4lb/ft 3 pleasedeterminetheheightof water,h,thatwillplacethetriangularblockinastateofimpendingtippingaboutpointo(6 points) 2a. x c=ft. y c=ft. 2b. h=ft. 5 ft y h O 3 ft x
Name (Last)(First) 2c.PleasestateNewton sthreelawsinorder(6points) 1 st Law 2 nd Law 3 rd Law
Name (Last)(First) 4.Thefootpedalisusedtosupportthemass(m=100kg).Notethatthefootpedalisan angledbracketthatconsistsofpointsb,c,andthepointatwhichtheloadisapplied. 4a.Drawafreebodydiagram(withanappropriatecoordinatesystem)ofthefootpedal(B C loadapplicationpoint).notethattheinteriorshaft(denotedbyhiddenlines)isa frictionlesssurfacethatprovidesanegligibleforcetokeepthesystemaligned.(6points) 4b.Determinetheforce,P,requiredtosupportthe100kgload.(5points) 4c.CalculatetheforceinlinkAB.Isitintensionorcompression?(3points)
Name (Last) (First) Problem 1a (4 points) Please denote all the ZERO FORCE members in the truss below: Zero Force Members are: Problem 1b (6 points) Please state Newton s Laws in order as succinctly as possible: Newton s First Law Newton s Second Law Newton s Third Law
Name (Last) (First) 2. The mechanism below is a model of a can crusher built by students in a basic mechanisms class. The slider mechanism is constructed with link ABC connected to link BD at a pin joint. A slider is attached at point D and slides along the horizontal surface with negligible friction. The force to crush a can is represented by force P (the force the can pushes back on the mechanism). The input to crush the can is force F = 40 lb which acts horizontal to the plane of mechanism. Please show all your work. i. (2 points) Please list all (if any) two force members here. ii. (3 points) Provide a free body diagram for the entire mechanism (please use the figure provided on the next page). iii. (5 points) Provide a free body diagram for the broken up mechanism (please use the figure provided on the next). iv. (10 points) Please determine the reactions at A, and the reaction P for the 40 lb input at the angles shown. Please provide answers here: a. A x = b. A y = c. M A = d. P =
Name (Last) (First) Please show work for Part ii here Please show work for Part iii here
Last Name:, First Name: 1. The truck shown below is connected to a tree. The angle, θ is 35 o, d1 = 1.8 m, d2 = 1.2 m and the truck weighs 12,000 Newtons. You may assume that the pulley at point B is an ideal pulley. 1a. Draw a free body diagram of the truck assuming that the wheels are free to roll (i.e. the brakes are not engaged). (5 points)
Last Name:, First Name: 1b. If the center of mass is a distance, h1 = 0.45 m above the ground and the cable (which is parallel to the hill) is h2 = 0.4 m above the ground, determine the tension in the cable BC. (5 points) 1c. Draw a free body diagram of the truck assuming that the front wheels are free to roll, but the rear wheels are locked (the coefficient of static friction, µs = 0.65). (4 points) 1d. If the back wheels are just on the verge of slipping, what is the tension in the cable BC? (6 points)
Last Name:, First Name: 2a. The basketball goal shown below is supported at point O by a cantilevered (also known as a fixed or built- in) support. The vertical beam weighs 65 lbs., the horizontal beam weighs 18 lbs. and Dr. Nauman (200 lbs.) is hanging on the rim at point B. The dimensions z1 = 10 ft., y3 = 4 ft., and y2 = 5 ft. You can neglect the weight of the rim and backboard. (10 points) First, draw a free body diagram of the basketball goal support system. Second, determine the reactions at point O. Free Body Diagram
Last Name:, First Name: Problem 3 A simple machine is shown below. A distributed load acts on member AB as shown. Pin joints connect link AB to the wall, link AB to BC, and link BC to the wall on the right. Ignore the masses of the links; the length of member BC is 3 meters. Please use the answer box provided on the following page: a. (3 points) Determine the equivalent force, F r, that can used to replace the distributed load. b. (2 points) Determine the distance from A (along AB) that the equivalent force, F r, will act. c. (5 points) Draw a free-body diagram for each member in the box provided using the members provided, REPLACE the distributed load with a properly located equivalent force. d. (4 points) Determine the magnitude of the force in member BC. e. (2 points) Is the member BC in compression or tension? f. (4 points) Determine the reactions pin joint A in Cartesian coordinates.
Last Name:, First Name: Answer Box (a) Fr = (b) Distance Fr acts from point A (c) C A B B Y (d) Magnitude of force in BC: X (e) Is BC in tension or compression? (f) Reactions at pin joint A expressed in Cartesian Coordinates (vector form):
Last Name:, First Name: 4c. Please state Newton s laws in order and as succinctly as possible. (4 points) I. II. III.
Last Name, First Name 2. Short answer questions 2a. (5 points) Shown below is a single blade wind turbine. The wind causes a drag force on the blade, F 1, in the x direction and a lift force, F 2, in the y direction that causes the blade to spin. You may assume that the forces act at the midpoint of the blade. If d 1 = 20 m, d 2 = 65 m, d 3 = 5m, F 1 = 45 N and F 2 = 225 N, determine the moment that the wind forces cause about the center of the rotating shaft (the origin of the coordinate system). What is the moment about the base of the tower? z y x F 1 d 1 F 2 d 2 d 3
Last Name, First Name Problem 3 (20 points). 3. Consider the A-Frame shown below. It is made up of three separate links, AC, CE, and BD. Link BD is attached to the other two with pins and it has a 500 lbs. load attached to it. Draw a free body diagram of the whole structure (4 points). Free body diagram of the whole structure.
Last Name, First Name Determine the reactions at A and E (3 points). Draw free body diagrams of each link. (7 points) Link AC Link BD Link CE Then determine the forces at points D and C. (6 points)