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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

### Euler's formula application

A pinned connected axially loaded steel bar is used as a compression member. The bar has a rectangular cross section 1 in. by 2 in. the proportional limit is 30,000psi. Calculate the minimum length for Euler's formula to be applicable, In addition calculate the critical stress and the critical load if the length of the bar is 5

### 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 ]

### Vertical Columb & Compressive Strength

A vertical column has the cross-sectional area shown in Fig1. (dimensions mm). The column carries a vertical compressive point-load of 300kN at C. Calculate the following: 1. The second moments of area, Izz, and Ixx. 2. The maximum values of the compressive and tensile stresses. 3. The position of the cross section where

### Vibration and Time Response

Plot the response x of the 20kg body ( see figure 1, attached) over the time interval 0<t>/1 second. Determine the maximum and minimum values of x and their respective times. The initial conditions are X0=0 and dx/dt=2m/s.

### 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 (

### Tension and Force Exerted

A 1 kg collar C slides without friction along the rod OA and is attached to rod BC by a frictionless pn. The rods rotate in the horizontal plane. At the instant shown BC is rotating counterclockwise and the speed of C is 1m/s, increasing at a rate of 1.2m/s^2. Determine at this instant, a) the tension n rod BC, b) the force exer

### 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

### Shear stress calculation

The butt riveted joint shown below consists of two cover plates and three 8 mm diameter rivets in each main plate. (a) During testing, a tensile load is applied to the main plates. The load is increased until the joint fails at a load of 57.3 kN. Determine the ultimate shear stress of the rivet material. (see attachment fo

### 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

### Francis turbine rotation

1. Water flows at a rate of 19.8m^3/s through a Francis turbine rotating at 228rpm. At the inlet to the runner, the runner diameter is 1.8m, the blade length is 30cm, and the relative flow angle is 29 degrees, measured from the radial direction. The fluid leaves the runner without swirl, and the hub and tip diameters at runner e

### Stress and Rotation Angle of Two Steel Shafts

Two solid steel shafts (G = 11.2 x 106 psi) are connected by the gears shown. Ends B and D are fixed. Assume points A and C are where the gears meets the shafts. What is the maximum shear stress in shaft CD under the loading shown? Choose One: 7.832ksi 6.987ksi 6.443ksi 5.844ksi What is the angle through which end C r

### Direct Stress and Strain on Steel Rod

A steel rod having a cross-sectional area of 0.005m2 and length 3m is attached to supports. Find (a) the force exerted by the rod on the supports if the temperature falls 60 degrees and the supports are unyielding. and (b) the force exerted by the rod on the supports if they yield 0.0002m while the temperature raises 50 degrees.

### Bending of Beams

Determine the maximum tensile and compressive bending stresses (together with the positions at which they occur) in the beam shown in the file. (Figure 1). The beams cross sectional area is also shown in the file. (See Figure 2 in attachment).

### Complex Loading - Bending and Compression

A steel chimney is 28m high, 1.4m external diameter, and 20mm thick. It is rigidly fixed at the base and is acted upon by a horizontal wind pressure of intensity 1.1KN/m2 on the projected area. The steel weighs 74KN/m length. Calculate the maximum stress in the chimney at the base.

### B-Spline Curve

Answer the following questions for a nonperiodic B-spline curve of order 3 defined by the control points P0,P1,P2,P3. a- What are the knot values? b- How many different curves is the B-spline curve composed of? c- Expand the B-spline curve equation to get the separate equations of the curves in b.

### Find the isobars (curves of constant pressure)

Consider the scalar field (pressure field) given by the function f(x,y)=9x2 + 4y2 Q: Find the isobars (curves of constant pressure) and sketch some of them. Complete problem in attached file...

### Block Stopping on an Incline with Spring

The package slides down a ramp and contacts the spring at a velocity of 20 ft/s. The spring has a mass that can be considered negligible. The spring constant is 1800 lb/ft. How many inches does the spring compress in order to stop the package? (150 lb package) (See attached file for full problem description)

### Block on incline and block on pulley

The following pulley system is released from rest. The acceleration in ft/sec2 of block B is what? See attached

### 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

### Multi degree of freedom - determining equation of motion

A picture of the system has been attached. There is no friction between m and m1. How would you determine the coordinates to describe the system and the equations of motion?