Exam Study Notes

Part 1

• A team is designing a pedestrian bridge for a mall.

• The main beam has a cross-section of 4 inches by 4 inches and is 10 feet long.

• It must support loads up to 2,500 pounds and not deflect more than 2 inches.

• The problem asks for the minimum modulus of elasticity (in psi) for the beam.

• An angled force of 400 pounds is applied at a 40° angle.

• The problem asks for the scalar value of the y-component in the vector, rounded to the nearest whole number.

  • The y-component of the force is $400 \cdot sin(40^{\circ})$.
  • $400 \cdot sin(40^{\circ}) \approx 257.115$, which rounds to 257 lb.

Part 2

• A mechanical engineer at Company A designs knee replacement units.
• The engineer signed an agreement not to share designs with competing companies if they leave.
• The engineer is considering leaving Company A because their boss disregards their ideas.
• The engineer accepts a new position at Company B in their hip division.
• Company B is reverse-engineering a new knee replacement unit that the engineer helped design at Company A.
• Company B obtained prototype units from inside connections, including a consultant and a former Company A employee.
• The question asks about ethical actions under these circumstances.
• Ethical considerations:
  • Learning about competitor's product features is ethical.
  • Identifying ways for your product to effectively work with a competitor's product is ethical.
  • Incorporating a feature protected by patent into your product's design is unethical.
  • Incorporating a feature from a competitor's product to make your product cheaper is unethical.
• Company B obtained knee replacement units via different methods:
  • Open market purchase.
  • From an orthopedic surgeon (consultant).
  • From a former Company A employee.
  • The ethically correct method is the open market purchase.
• Specialists and their activities in knee replacement development:
  • Material scientist: Develops biocompatible components that minimize adverse reactions.
  • Electrical engineer: Creates a device to detect nerve signals and convert them to digital information.
  • Industrial engineer: Creates an efficient sterile manufacturing process to minimize infection risk.
  • Computer scientist: Writes a program that converts and tabulates digital information from a medical device for a medical professional to interpret.
  • Mechanical engineer: Analyzes how the forces associated with different motions are distributed throughout the device.

Part 3

• A hydraulic lift is designed to lift a 3,000-pound car.

• The diameter of the cylinder under the car (Piston 2) is 3 feet.

• The diameter of the cylinder at Piston 1 is 6 inches (0.5 feet).

• The problem asks for the area of each piston in square feet.

• Area calculations:

  • $A = \pi r^2$, where $r$ is the radius.
  • For Piston 1: $r = 0.5 / 2 = 0.25$ ft, so $A_1 = 3.14 \cdot (0.25)^2 = 0.19625 \approx 0.2$ ft².
  • For Piston 2: $r = 3 / 2 = 1.5$ ft, so $A_2 = 3.14 \cdot (1.5)^2 = 7.065 \approx 7$ ft².

• The correct answer is $A<em>1 = 0.2$ ft² and $A</em>2 = 7$ ft².

• The problem asks for the pressure exerted by Piston 2 on the hydraulic liquid.

• Pressure calculation:

  • $P = F / A$, where $F$ is force and $A$ is area.
  • $P = 3000 \text{ lb} / 7 \text{ ft}^2 = 428.57 \approx 429 \text{ lb/ft}^2$.

• To convert lb/ft² to psi: $428.57 \text{ lb/ft}^2 / 144 \text{ in}^2/\text{ft}^2 = 2.976 \text{ psi}$.

• The problem asks how much work Piston 1 does to lift the car 2 feet.

• Work calculation:

  • Work = Force x Distance. Since the output force is 3000 lbs, and the car is lifted 2 feet, the work done is $3000 \times 2 = 6000$ ft-lb.

• The problem asks for the mechanical advantage of the hydraulic system.

• Mechanical advantage calculation:

  • Mechanical Advantage (MA) = Output Force / Input Force = Area2 / Area1 = 7 / 0.2 = 35.

• The problem describes a leak in the main line and asks for the new line diameter.

• Given flow rate $Q = 2500$ cubic inches per minute and flow velocity $v = 795$ inches per minute.

  • $Q = A \cdot v$, where A is the cross-sectional area of the pipe.
  • $A = Q / v = 2500 / 795 = 3.14465 \text{ in}^2$.
  • Since $A = \pi r^2$, then $r = \sqrt{A / \pi} = \sqrt{3.14465 / 3.14} \approx 1 \text{ in}$.
  • Diameter $d = 2r = 2 \cdot 1 = 2$ inches.

Part 4

• The scenario involves a high-performing engineer selected for a leadership program to develop an energy-efficiency project.
• The initial meeting conflicts with a doctor's appointment the engineer has had for months.
• The team appears unwilling to adjust the meeting time.
• Appropriate response: Inform the team of the conflict and request meeting minutes.
• Another team presented, but their presentation was incomplete. Critical information that should have been included:
  • Cost savings.
  • Project timeline.
  • Design statement.
  • Current company issues.
• The engineer's team performed well and was selected to redesign the company's flagship product to reduce costs.
• The first task should be to analyze the current product.
• Proper citation is important in redesigning the company's product.
• Items that should be cited include:
  • Sketches published in an online article.
  • Charts and graphs from a science journal.
  • Quotes from an interview with a research professor.

Part 5

• A lever in static equilibrium is shown.

  • $F_E$ is the effort force.
  • $F_R$ is the resistance force.
  • $D_E$ is the effort distance.
  • $D_R$ is the resistance distance.
  • $F<em>R = 100$ lb, $D</em>R = 4$ in, $D<em>E = 12$ in, $F</em>E = 50$ lb.

• Ideal mechanical advantage (IMA) calculation:

  • $IMA = D<em>E / D</em>R = 12 / 4 = 3$.

• Actual mechanical advantage (AMA) calculation:

  • $AMA = F<em>R / F</em>E = 100 / 50 = 2$.

• Efficiency percentage calculation:

  • $\text{Efficiency} = (AMA / IMA) \cdot 100\% = (2 / 3) \cdot 100\% = 66.66\% \approx 67\%$.

• Reasons for efficiency greater than 100%:

  • Incorrect values for the resistance distance.
  • Inaccurate readings from force sensor for effort force.

• Factors affecting efficiency:

  • Increase/decrease $F_R$: Affects efficiency.
  • Increase/decrease $F_E$: Affects efficiency.
  • Change the weight of the lever: Does not affect efficiency.
  • Adjust the friction at the pivot point: Affects efficiency.

Part 6

• The problem concerns a truss structure.
• Assumptions for solving forces in internal truss members:
  • All members are perfectly straight.
  • All joints are pinned and frictionless.
  • Members can only experience tension or compression forces.

Part 7

• The main difference between an open loop and a closed loop is that a closed loop is controlled by sensor input – not wait times.
• Open loop: Using wait time to control the distance a motor goes.
• Closed loop: Using an encoder to determine when the motor has reached a specific distance.

Part 8

• A new industrial building needs a power line.
• The project involves acquiring land, designing power poles and wire, and designing the substation.
• The engineering discipline least likely to be required is chemical engineering.
• Matching design process steps with tasks:
  • Define problem: Identify criteria and constraints.
  • Generate concepts: Collect and analyze data.
  • Develop a solution: Create technical drawings.
  • Evaluate solution: Construct and test prototype.
  • Present solution: Document and communicate the project.

Part 9

• A toy car is tested, and axle pins break at 50 pounds of force.

• The prototype has axle Form 1 and Material A.

• Free-body diagram required for the wheel and axle system.

• The length of the axle between two wheels is 3.5 inches.

• Moment on one wheel:

  • Force = 50 lb is applied. Radius arm is half the axle length = 3.5/2 = 1.75 inches
  • Moment = Force * radius = 50 lb * 1.75 inches = 87.5 in-lb
  • Convert to foot-pounds: 87.5 in-lb / (12 in/ft) = 7.29 ft-lb

• Tensile testing of axle materials.

• The problem requires ranking materials by modulus of elasticity.

• Design changes to withstand increased force:

  • Double the axle radius.
  • Halve the axle length.
  • Double the axle tensile strength.

Part 10

• NASA evaluates materials for the International Space Station after a hole was discovered.
• Materials X, Y, and Z are tested for beam deflection at 2,000 lbf and 4,000 lbf.
• The problem requires identifying the material with the largest beam deflection at 2,000 lbf.
• Stress-strain curves are created for each material.
• The problem requires identifying the material that can handle the highest force without permanent deformation.

Part 11

• A truss diagram is shown.

• Determining whether to include or exclude reaction forces from the drawing:

  • Reaction Force: Included
  • $R<em>{AX}$, $R</em>{AY}$, $R<em>{CX}$, $R</em>{CY}$

• Moment equilibrium equation around point A to calculate $R_{CY}$. Given AB = 20 ft and BC = 30 ft.

  • $\sum M<em>A = 0 = -(500 \text{ lb} \cdot 20 \text{ ft}) + R</em>{CY} \cdot (20 + 30) \text{ ft}$
  • $R_{CY} = (500 \cdot 20) / 50 = 200 \text{ lb}$.

• Calculate the magnitude of vector a, given $a_y = 300 \text{ lb}$ and $\theta = 40^{\circ}$.

  • $sin(\theta) = a_y / a$
  • $a = a_y / sin(\theta) = 300 / sin(40^{\circ}) \approx 466.7 \text{ lb}$. Rounded to the nearest whole number, $a = 467 \text{ lb}$.