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# Mechanical Engineering

### Bullet and Wood Block Problem

A bullet is fired horizontally into a wood block resting on a horizontal, frictionless surface. If the mass of the bullet is 0.02 Kg and the velocity is 600 m/s, what is the velocity of the wood block after the bullet is embedded in it? Assume the wood block has a mass of 50 kg. a. 1 m/s b. 2 m/s c. 2.5 m/s d. 0.24 m/s

### Time & Distance Before a Car Stops

A brake is applied to a car traveling at a constant speed of 25 m/s. If the deceleration caused by the braking action is 5 m/per second squared, find the time before the car stops. a. 1s b. 2s c. 4s d. 5s Determine the distance traveled before the car stops, IF the car stops at t = 5 seconds. a. 52.5 m b. 62.5 m c. 25

### Kinetic Energy & Stopping Force of a Car

A car of mass 1500 kg is moving with a speed of 50 km/h (13.89 m/s). Determine the kinetic energy T of the car. (see options a through d in attached file) Now determine the force required to stop the car at a distance of 50 m, if the kinetic energy T is 1.447 x 10E5 N-m. 10E5 means 10 to the 5th power. a. 1447 N b. 289

### Determining Time to Reach Maximum Height

A ball with a mass of 0.25 kg is thrown vertically upward with an initial velocity of 10 m/s. What is the velocity of the ball when it reaches the highest point? a. 10 m/s b. 0.25 m/s c. 0 m/s d. Can not be determined How many seconds would it take for the ball to reach its maximum height. a. 10s b. 1.02 s c. 0.25 s d

### Inverse Laplace Transform

Inverse Laplace Transform. See attached file for full problem description.

### Laplace transform of unit impulse

See attached file for full problem description. a. b. 1 c. d. 0

### Two flat, rectangular plates with a lateral dimension

Two flat, rectangular plates with a lateral dimension w*l lie parallel, one above the other, a distance h apart. The gap between them is filled with molten polymer. One plate is fixed; the other moves parallel to it in the direction of the dimension l at velocity v, causing the fluid to be sheared. Show that the fluid is displac

### 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

### Axial compressive load - southern pine column

Design a square or rectangular (2-in. nominal increments) pin-connected southern pine column (S4S). The unbraced length of the column is 16ft. The column is to support an axial compressive load of 60,000 lbs.

Select the lightest W shaped for a column subjected to an axial compressive load of 6000 kips. The unbraced length of the column is 15ft and the ends are fixed/pinned.

### 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

### Max load calculation for a steel pipe

A section of 51 mm diameter standard-weight steel pipe is bent as shown in the figure below and embedded in a concrete footing. Calculate the maximum load P that may be applied if the allowable compressive stress at point B is 80 MPa

### 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 ]

### Maximum Horizontal Shear and Bending Stress

See the attached file. 3. A 4 inch diameter solid circular shaft has a V-belt pulley attached to one end and is supported as shown below. The combined pulley weight and belt pull is 1000 lbs. Determine the magnitude and location of the: (a) maximum horizontal shear stress (b) maximum bending stress Neglect the shaft wei

### 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.

### Flow and Momentum

A hot gas stream enters a uniform diameter return bend as shown. The entrance velocity is 100 f/s, the gas density is .02lbm/cubic ft. and the mass flow rate is 1 lbm/cubic ft. The gas is cooled before exiting the bend and exits the bend at a density of .06 lbm/cubic ft. The pressures at the entrance and exit of the bend are equ

### 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.

### Shear Force and Bending

The beam shown below is simply supported at its ends A and E. It carries a load that is uniformly distributed over part of the beam together with two concentrated loads: (See attached file for full problem description with diagram) Using convenient scales, construct the Shear Force and Bending Moment diagrams for the beam and

### Altimeter Reading at Sea Level

Please provide some help with this problem, the answer is 5186m, 16.6m below sea level but I need to understand why: An aeroplane is fitted with an altimeter calibrated assuming the atmosphere meets the ISA specification. On a day when sea level pressure and temperature are 101,500 N/m2 and 25 degrees the altimeter reads 5000

### What is the output horsepower? Efficiency?

If a fully loaded 440V, three-phase motor draws 12.4 A at 86% power factor (pf). It's speed is 1730 rpm and its torque output to a mechanical load is 29.1 lb-ft x 1.356 = 39.5 Nm. What is the output horsepower? Efficiency?

### Cavitation Problem in a Sphere

A sphere 1 foot in diameter is moving at a depth of 10 feet below a water surface where the water temp is 50 degrees F. At what speed will cavitation first appear? Please show work and any assumptions.

### 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

### Maximum flow around a circular cylinder

The maximum flow past a circular cylinder is 2 X the Up stream velocity. The max velocity occurs at the center line of the top of the cylinder. Assume std pressure and Temp for air and irrational flow. What is the difference between the lowest and highest pressures? The cylinder is suspended in a 40/m wind.

### 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 (

### Diffusion Coeffiecient, Calculate Constant

The diffusion coefficient for Cr^+3 in Cr2O3 is 6x10^-15 cm2/s at 727 degrees Celcius and is 1x10^-9 cm2/s at 1400 degrees Celcius. Calculate the constant D0. Use the value of the Gas constant R+1.987 cal/mole.K a) 0.015 cm2/s b) 0.055 cm2/s c) 0.25 cm2/s