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# Mechanical Engineering

### Mechanics of Materials and Critical Loads

A hollow brass rod is pin jointed and loaded in compression as shown. Knowing that the length L = 3 m, outside diameter D = 60 mm, and the wall thickness t = 10 mm Determine the critical load P. Use E = 105 GPa Choose One: 84.8kN 72.4kN 58.8kN 45.2kN Determine the normal stress at the critical load. Choose One: 32.1

### Mechanics of Materials and Reaction Force

For the beam and loading shown, determine the reaction force at end A Choose One: 12kN 40kN 36kN 8kN For the beam and loading shown, determine the reaction force at end B Choose One: 12kN 40kN 36kN 8kN (See attached file for full problem description and diagram)

### Mechanics of Materials: Slope & Deflection

A) For the cantilever beam and loading shown, determine the slope at point B. Use E = 29,000,000 psi Choose One: .0021rad .0051rad .0175rad .0196rad b) Determine the deflection at point B Choose One: .113in .285in .424in .625in

### Deflection Mechanics of Materials

The rod ABC is made of steel (E = 29 x 106 psi). Determine the deflection at point B. Choose One: .002in .004in .006in .008in Determine the deflection at point C. Choose One: .013in .017in .024in .029in Determine the normal stress in section BC Choose One: 10.47ksi 14.38ksi 16.75ksi 18.31ksi

### 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.

### Vector integral - stokes therom

Evaluate the line integral by stokes theorem (clock wise as seen by a person standing at the origin). Calculate this integral by stoke's theorem for the following C and F (referred to right-handed cartesian coordinates). F=[y, 1/2 z, 3/2 y] C the circle x^2 + y^2 +z^2 = 6z, z=x+3

### Midpoint of a Bezier Curve and Arc

Determine the Bezier curve of order 3 that approximates a quarter circle centered at (0,0), (1,0), (0,1). a) Calculate the coordinate of the middle point on the Bezier curve and on the arc and compare them (I have already calculated the midpoint of the arc which is 0.5, 0.5 and the Bezier curve is supposed to be about the sam

### 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.

### Average Potential Energy for Electron

Just some analysis/explanation please. (See attached file for full problem description).

### Finding Center of Gravity using Double Intergral

Find the coordinates x*,y* of the center of gravity of a mass of density f(x,y)=1 in a region R, where R is a triangle with vertices (0,0), (b,0), (b,h).

### Centrifugal pump analysis performance

A centrifugal pump is run under test at 1500 rev/min and returns the following performance figures... The pump is required to transfer water from a lake to a reservoir with a water level... See attached file for full problem description

### 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...

### Resistance of Copper Wire

See the attached file. a) What is the resistance of the wire? (see attachment for diagram and full questions) b) If a voltage of 1mV=10^-3volts is applied across the wire, what is the current (I) and current density (J) along the wire? c) Taking 1 electron per atom as conducting (we will justify later, why most of the C

### Psychometry Problem for a Precision Gauge Laboratory

In the attached problem, there is a solution to part a attached. Please solve part b completely. In an air conditioning system for a precision gauge laboratory, atmospheric air at 32 C, 101.3 kPa and 80% relative humidity is first chilled to 10 C to remove moisture.

### 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

### Rotation bars and slider

Rod AB is rotating 4rad/s clockwise. The speed in m/s of the slider is what in m/s? (See attached file for full problem description)

### 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

### Tensile force formulas

A cylindrical steel beam is 2 inches diameter and 6 feet long. The modulus of elasticity is 30 x 1,000,000 psi. If the beam is subjected to a tensile force of 1000 lbs, what will be the resulting unit strain? A. 16,000 psi B. .002 ft-lbs/sq-in C. 0.000064 ft/ft D. .0000106 in/in

### Relative Acceleration of two cars

Two cars split onto seperate roads. One goes straight and the other peels ot the right. What is the acceleration of B with respect to A in mi/hr^2 at the point shown in the figure? --- (See attached file for full problem description)

### Pulleys with an Acceleration Component

A pulley system is released from rest. Find the acceleration of both of the weights on the pulleys. --- (See attached file for full problem description)

### Maximizing a function - mechanical

What value of x will maximize: r(x)=r^2*(ln(1/x)? x can take values between 1/4 and 1

### 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?

### 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

### The problem is from Math for Engineers in Undergraduate 400 level.

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. If there is anything unclear in the problem, let me know. Thank you. (See attached file for full problem description)

### SLENDER BAR ANGULAR ACCELERATION

The two 10-Kg slender bars (10-m long each) are released from rest in the position shown. Assuming the floor to be smooth, determine the angular acceleration of the bar AB, right after release. See attached

### PENDULUM

A pendulum consists of a uniform 10-lb plate and a 3-lb slender rod, the whole system swinging around a pin at 0 as shown. At the instant shown (theta = 30) the pendulum has a counterlockwise angular velocity of 5 rad/s. Determine the pin reactions at 0. see attached