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# Mechanical Engineering

### Bullet Final Velocity in Water

A bullet is fired into water with an initial velocity of 60m/s. Acceleration = -0.4v^3 m/s^2. Find the velocity of the bullet and the distance it has traveled into the water after 4 seconds. Please show detailed step by step process to solution.

### Mechanical Vibrations

1) A machine tool having a mass of 1000 kg and a moment of inertia J = 300 kg-m2, is supported on elastic supports with stiffness's and locations shown. i) Find the natural frequencies of the machine tool. ii) What are the corresponding amplitude ratios? (There are 2 separate questions in 1 problem). Please see attached

### Finding Magnification factor M for Frequency Ratio

1) In the idealized model attached shown, m = 15 kg, k = 135 N/m, and the viscous damping ratio is 0.15. Assume that an external harmonic force F(t) = 15 cos 4 t acts on the system with F0=15 N and forcing frequency of 4 rad/s. i) Find the magnification factor M for the frequency ratio r of 1.382. ii) What is the amplitude o

### Matrix equation of motion

1) For the two degree of freedom structure shown: i) what is the matrix equation of motion?. Assume that m1 and m2 oscillate harmonically with the same frequency but with different amplitudes X1 and X2 of x1(t) and x2(t). ii) what are the values of the amplitude ratios r1 and r2 if m1 = m2 = m, k1 = k, and k2 =3k? See a

### Advanced dynamics and mechanical vibration

Advanced dynamics. See attached file for full problem description.

### The compression ratio of an air-standard Otto cycle is 9.5

The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at 100 kPa, 17 C, and 600 cm2. The temperature at the end of the isentropic expansion process is 800K. Using specific heat value at room temperature, determine: 1. The highest temperature and pressure in the

### Flow Rate - Manometer

Water flows through the pipe contraction shown in the figure below. For the given 0.2 m difference in the manometer level, determine the flowrate as a function of the diameter of the small pipe, D. See attached file for full problem description.

### Dynamics Projectile Problem

A hunter in the plains of Africa is equipped with a bow and arrow. The maximum range of the bow is 100 m. If a Lion charges straight towards him at 30 km/h and the hunter aims his bow at 20 degrees relative to the horizontal, find: (a) time of flight of the arrow (b) arrow velocity (c) how far away should the lion be when t

### A Tricky String Pulley Problem in Dynamics

Problem # 2 - If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at Which block B rises. Give logical explanation i.e. qualitative as well as quantitative way. For figure, please see attached file.

Collar C slides relative to the curved rod at a constant speed u, while the rod rotates about the horizontal axis at the constant rate. Determine the acceleration of the collar in terms of theta.

### A turbine salesman makes the following claim

A turbine salesman makes the following claim for one of his products: Steam enters a steady-flow adiabatic turbine at 4 MPa, 600 °C with negligible velocity and exhausts at 200 kPa with a velocity of 180 m/s. The flow rate is 2.2 kg/s and the turbine power is 2 MW. a. If the turbine operated as described by the salesman, w

### Refrigeration cycles

A refrigeration system using refrigerant 22 is to have a refrigerating capacity of 80 kW. The cycle is a standard vapor-compression cycle in which the evaporating temperature is -8 degrees Celsius and the condensing temperature 42 degrees Celsius. (a) Determine the volume flow of refrigerant measured in cubic meters per seco

### Refrigerant 134a enters a heat exchanger in a steady state refrigeration system as saturated

Refrigerant 134a enters a heat exchanger in a steady state refrigeration system as saturated vapor at 0 °F and exits at 20 °F with no change in pressure. A separate liquid stream of Refrigerant 134a passes in counterflow to the vapor stream, entering at 105 °F, 160 psia and exiting at a lower temperature while experiencing n

### Energy Analysis Of Closed Systems

A 4 x 5 x 7 m room is heated by the radiator of a steam heating system. The steam radiator transfer heat at a rate of .... Please show all work step by step and include all applicable formulas. (See attached file for full problem description)

### Energy Analysis or a Closed System Piston

Hydrogen is contained in a piston-cylinder device at 14.7 psia and 15 ft3. At this state , a linear spring (F x) witha spring constant of 15,000 lbf/ft is touching the piston but exerts no force on it. The cross-sectional area of the piston is 3 ft2. Heat is transferred to the hydrogen, causing it to expand until its volume dou

### Determining the exit velocity from an air nozzle

Air enters a nozzle operating at steady state at 800 ºR with a negligible velocity and exits the nozzle at 570 ºR. Heat transfer occurs from the air to the surroundings at a rate of 10 Btu per pound of air flowing. Assuming ideal gas behavior and neglecting potential energy effects, determine the velocity at the exit in ft/s.

### Refrigerant R-134a vapor in a piston-cylinder assembly

Refrigerant R-134a vapor in a piston-cylinder assembly undergoes a constant-pressure process from saturated vapor at 800 kPa to 50 ºC. For the refrigerant, determine the work and the heat transfer, per unit mass (each in kJ/kg). Changes in kinetic and potential energy are negligible.

### A piston-cylinder device initially contains 50L

A piston-cylinder device initially contains 50L of liquid water at 40 degrees C and 200kPa. Heat is transferred to the water at constant pressure until entire liquid is vaporized. (a) What is the mass of the water? (b) What is the final temperature? (c) Determine total enthalpy change. (d) Show process on a T-v diagram with

### A piston-cylinder device contains 0.8kg of steam at 300 degrees C and 1 MPa

A piston-cylinder device contains 0.8kg of steam at 300 degrees C and 1 MPa. Steam is cooled at constant pressure until one-half of the mass condenses. (a) Show the process on a T-v diagram. (b) Find the final temperature (c) Determine the volume change.

### A 7 cm orifice meter is being used to measure the flowrate

A 7 cm orifice meter is being used to measure the flowrate of 50C water. The mercury manometer shows a height of ... (See attached file for full problem description)

### 350 gpm of 120F water are being pumped through the system

350 gpm of 120F water are being pumped through the system shown. All pipe is 4" copper tubing. (See attached file for full problem description)

### Gasoline at 30C flows upward from the 2" schedule 40

Gasoline at 30C flows upward from the 2" schedule 40 steel pipe to the 30" schedule steel pipe. (See attached file for full problem description)

### Buoy Problem - Center of Gravity

(See attached file for full problem description) A cylindrical buoy two meters in diameter and six meters high is floating upright in seawater as shown at 20 degrees C. The buoy contains weather recording instrumentation and has a mass of 12,000 kg. Its center o gravity is 2 meters above the bottom. a) Determine the depth

### Psychrometry

Please solve the problem using an atmospheric pressure of 85 kPa. Do not use a psychrometric chart but from first principles using formulae. I think you need to use steam tables: In an air-conditioning unit 3.5 m^3/s of air at 27 degrees Celsius dry-bulb temperature, 50% relative humidity and standard atmospheric pressure enter

### A gas turbine takes in air at 300 K and discharges it to the combustion chamber at 620 K

A gas turbine takes in air at 300 K and discharges it to the combustion chamber at 620 K. See attached file for full problem description with diagram. Determine: a/ the theoretical compressor power input b/ the theoretical turbine power output c/ the thermal efficiency of the turbine d/ the work ratio of the turbine

### Power transmission velocity

(See attached file for full problem description) A four car linkage is shown in the attachment. The crank OA, the connecting rod AB, and the rocker BC are 20mm, 120mm, and 60mm long respectively. The crank rotates at a speed of 60 rpm and the centre distance OC is 90mm. At the instant shown determine: (I) The velocity of C

### Components and Force of a Timber and a Wall

A timber of uniform cross section with a mass of 90 kg is hinged at its lower end and held at angle of 60 degrees with the horizontal by a rod attached as shown in (attached figure 4-6) A cylinder which has a mass of 30 kg is placed between the timber and the wall. 1) What are the horizontal and vertical components of the r

### Estimate the ultimate steel strength

A steel member has a Brinell of HB =250. Estimate the ultimate strength Su of the steel in MPa. a. 852.5 MPa b. 250.5 MPa c. 100.5 MPa

### 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

### 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