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Mechanical Engineering

Mechanical Vibrations Questions

(See attached file for full problem description with diagrams) Mechanical Vibrations Question No.1 A pulley 250mm in diameter drives a second pulley 1000mm diameter by means of a belt.The mass moment of inertia of the drive pulley is 0.2kg-m2. The belt connecting these pulleys is represented by two springs, each of stiffness

Stress Due to Axial Force and Bending Moment

A circular cross section solid steel shaft 3" in diameter and 4 feet long is fixed at one end and free at the other. As shown in the figure below, the shaft is subjected to an axial tensile load of 50,000 lbs. If the force P = 390 lbs, what is the combined stress at point A and point B. Indicate whether they are compressive o

Strength of material using the Paris Law

(See attached file for full problem description with equations and diagram) --- Practice problem for Fracture and Fatigue. Adapted from S. Suresh, Fatigue of Materials, second edition, Cambridge University Press Publishing. Consider an aircraft fuselage, existing like a cylindrical pressure vessel. Every day, this aircr

Solving for the equation of a cubic b-spline curve

Find the equation of a cubic B-Spline curve defined by these control points. See separate file attached with problem set up. Coordinates of four control points given here: P0 = [ 2 1 0 ] P1 = [ 2 3 0 ] P2 = [ 3 2 0 ] P3 = [ 3 4 0 ]

Linear Equations and Outputs

An AC sine wave is applied to the input of a full wave rectifier. The output of the full wave rectifier is then applied to a half wave rectifier. The output of the half wave rectifier will most closely resemble: A) the original sine wave. B) an inverted form of the original sine wave. C) the output of the full wave rectifier.

Aircraft acceleration and time

An aircraft accelerates uniformly from rest down a runway. After a distance of 800m, the aircraft reaches its take-off speed of 288 km/h. (a) What is the acceleration of the aircraft (in m/s2)? (b) How long does it take the aircraft to reach its take-off speed? Please provide equations and solutions.

Hoist drum questions

A hoist drum consists of a uniform cylinder of diameter 1.2m, radius of gyration 0.45m and mass 200kg. It is being used to lower a crate of mass of 60 kg which is attached to the hoist by a light, inextensible rope. Initially, the crate is at rest 3.0 m above the ground. A brake on the drum is accidentally partially released

Stiffness matrices and displacements in spring systems

For the spring system shown in the attached diagram, find: a) The stiffness matrix for each element b) The unconstrained global stiffness matrix c) The constrained (reduced) stiffness matrix d) The displacements of node 2 and node 3 e) The reaction forces at node 1 and node 4 For the given spring system in the second at

Carbon Content of Steel

A steel contains 55% alpha-ferrite and 45% gamma-ferrite or austenite at 750 degrees Celsius. What is the carbon content of steel? a) 0.25% b) 0.5% c) 0.28% ****This is how the problem was written however I'm not sure if it makes sense that 55% and 45% are supposed to be 0.55% and 0.45%**** My guess at the answer is (

Newton Laws, conveyer belt

1. A package is at rest on a conveyer belt which is initially at rest. The belt is started and moves to the right for 1.5s with a constant acceleration of 3.2m/s^2. The belt then moves with a constant deceleration a_2 and comes to a stop after a total displacement of 4.6m. Knowing that the coefficients of friction between the pa

Working Speed in RPM

A transmission shaft is fitted with a coupling that is secured by eight 20 mm diameter bolts pitched on a circle with a diameter of 225 mm. The bolt material has an ultimate shear stress of 280 MN/m2 and a factor of safety of 4.0 is to be used. If the power being transmitted is 1.8 MW, determine the working speed of the shaft in

Process Design - Assembly Line

#1.) An assembly line is to operate 8 hours per day with a desired output of 240 units pr day. The following table contains information on this product's task, task time, and precedence relationship. (see attachment) a.) Design an assembly line that is capable of achieving the desired output rate with the fewest number

Motor and power cuts

A motor is running at 12 rpm and the switch is flipped and cuts the power. The rotor weighs 75 lbs. The radius of gyration of the rotor is 6``. The rotor experiences an average friction moment 6 lb/in. How many seconds does it take for the rotor to come to rest?

Compressive stress

A circular cross sectional bar with a diameter of 3.25 inches is loaded with a uniform axial compressive load of 22,750 pounds. What is the compressive stress along a cross section of the bar? A. Cannot be determined because the length of the bar is unknown B. Over 10,000 psi C. Less than 1,000 psi D. Between 2,000 and 9

Workout velocity and range of shell fired

1. Why is it possible to consider the vertical and horizontal motion of a projectile independently of each other. 2. A mortar shell fired with an angle of elevation of 50 degrees ahs a range of 2.5 km. Neglecting air resistance determine: a. The time of flight. b. The shells initial velocity. c. The shells range and heig

Hazen-Williams Formula : Find the Diameter of a Pipe

The length of cast-iron pipe is to be 4200 ft., and the head causing flow is to be 12.6ft. After the pipe has been in service 5 years, it is expected to discharge water at a rate equal to 3.2 cfs. Using a Hazen-Williams Formula Chart in which C = 160 What is the diameter of the pipe? 16 in., 12 in., 14 in., 10 in. The head fl

Heat pump for house

Ever wonder if you can build a machine to heat up your house using the heat from the outside environment? Well you'll need to start with the heat pump concept. In this example, you'll learn how to determine the maximum theoretical coefficient of performance for a heat pump operating at steady state between a dwelling at 70 de

Water is the working fluid in an ideal Rankine cycle.

Water is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 18 MPa. The condenser pressure is 6 kPa. How do I determine the quality of the fluid at the turbine exit, and the heat transfer to the steam passing through the boiler in kJ per kg of steam flowing. The enthalpy of the steam entering the

Determining Feasibility

At steady state, a new power cycle is claimed by its inventor to develop 6 horsepower for a heat addition rate of 400 Btu/min. If the cycle operates between reservoirs at 2400 and 1000 deg R, is the claim feasible?

Determine the Mass of Ammonia

Ammonia is stored in a tank with a volume of 0.21 m^3. How do I determine the mass, in kg, assuming saturated liquid at 20 deg C.

Find the Temperature of the Refrigerant

A closed vessel with a volume of 2 ft^3 contains 5 lb of Refrigerant 134a. A pressure sensor in the tank wall reads 71.39 lbf/in.^2 (gage). If the atmospheric pressure is 14.4 lbf/in.^2 how do I find the temperature of the refrigerant, in deg F?

Determine the Final Velocity

An object whose mass is 1 lb has a velocity of 100 ft/s. How would I determine the final velocity, in ft/s, if the kinetic energy of the object decreases by 100 ft*lbf? What would be the change in elevation, in ft. associated with the 100 ft*lbf change in potential energy if g=32.0 ft/s^2?

Turbine Thermal Efficiency

Steam @ 10 MPa, 600 degrees celcius enters the first-stage turbine of an ideal Rankine cycle with reheat. The steam leaving the reheat section of the steam generator is @ 500 degrees celcius, and the condensor pressure is 5 kPa. If the quality at the exit of the second-stage turbine is 90%, determine the cycle thermal efficien

Mechanics of Materials

Question: Two full-size 2x6 inch planks are connected as shown by lag screws to form a beam which is subject to a vertical shear of 400 lb. Knowing that the allowable shearing force is 360 lb in each lag screw, how would I determine the largest permissible longitudinal spacing (s) of the lag screws, and the maximum shearing stre

Rigid Bodies and Newton's Second Law of Motion

The wheel and axle system shown attached in Figure Q2 supports a free hanging mass of 360g. The mass is initially a distance of 2.16m above the floor level when it is released causing the mass to hit the floor 6.2s later. The mass of the wheel and axle system is 40.2kg and its effective radius of gyration is equal to 2.8cm. (

Problems of Velocity, Angular Velocity and Acceleration in Trains and Wheels

Question 1: A train accelerates uniformly along a straight track and passes three trackside markers. The distance between the first two markers is equal to 0.25 km and between the second and third the distance is 0.4km. The train takes 26.6 seconds to travel between the first two markers and its speed as it passes the second ma

Force Required to Punch a Hole into an Aluminium Sheet

Question 4: (a) Calculate the force required to punch out a rectangular hole 100m x 50mm in a 2mm thick aluminium sheet. The ultimate strength in shear is 125 MN/m^2. (b) If the maximum force which can be exerted by the press is 45kN, what is the greatest thickness that can be punched out? Question 5: Two co-axial sha

Analyze the Planner Equilibrium

The roof truss shown attached is roller and pin-joint supported at the right-hand and left-hand ends respectively and carries loads of 10kN, 8kN and 12 kN as shown. Show that the structure is stable and determine, using the method of resolution of forces at the joints, the magnitude and nature of the forces acting in each of