Mechanical Engineering Answers

The center rod CD of the assembly shown in the figure is heated from T₁ = 30^oC to T₂ = 180^oC using electrical resistance heating. The two end rods AB and EF are heated from T₁ = 30^oC to  T₂ = 50^oC. At the lower temperature T₁, the gap between C and the rigid bar is 0.7 mm. Rods AB and EF are made of steel and each have a cross-sectional area of 125 mm². CD is made of aluminum and has a cross-sectional area of 375 mm². E_Steel = 200 GPa, E_Aluminum = 70 GPa,    α_steel = 12x10^-6/^oC, α_Aluminum = 23 x10^-6 /^oC.

Calculate the force and the stress in rods AB, EF and CD caused by the increase in temperature.  

A CEO of a well-known television show wants to build a new rectangular shaped acting stage. The width, thickness and length of the stage are 3 m, 0.2 m and 5 m, respectively. Both ends of the stage must be fixed. The stage should carry a musical instrument, and air conditioner of a total mass of 1500 kg and 800 kg at 1 m, and 2 m from the left end support. Such equipment acts as a concentrated loads on the stage that has a distributed load of 500 kg/m. The Young’s modulus of the material is 200 GPa. 1.1. Use the engineering sketch to illustrate the structure of the stage and calculate the transverse vibration frequency of the stage. (18) 1.2. Determine the amount of rection forces on the stage supports. 

A CEO of a well-known television show wants to build a new rectangular shaped acting stage. The width, thickness and length of the stage are 3 m, 0.2 m and 5 m, respectively. Both ends of the stage must be fixed. The stage should carry a musical instrument, and air conditioner of a total mass of 1500 kg and 800 kg at 1 m, and 2 m from the left end support. Such equipment acts as a concentrated loads on the stage that has a distributed load of 500 kg/m. The Young’s modulus of the material is 200 GPa.  

1.1. Use the engineering sketch to illustrate the structure of the stage and calculate the transverse vibration frequency of the stage.  (18)

1.2. Determine the amount of rection forces on the stage supports.  

One kilogram of gas at an initial pressure of 0.11 MN/m² and a temperature of 15⁰C.

It is compressed isothermally until the volume becomes 0.1 m³ .Determine

a) the final pressure

b) the final temperature

c) the heat transfer

If the compression had been adiabatic, determine

d) the final pressure

e)the final temperature

f) the work transfer

An engine has a swept volume of 15 litres and a volume ratio of compression of 14:1. The air in the engine at the beginning of compression has a temperature and pressure of 30⁰C and 95 kN/m², respectively. The air is compressed according to the law PV^1.34=C At the end of the compression the air is heated at constant volume through a pressure ratio of 1.6:1. Determine

a)the temperature and pressure of the air at the end of the compression

b)the temperature and pressure of the air at the end of the constant volume process

c)the heat transfer required to carry out the constant volume process

For the air, take c_p = 1.005 KJ/kg K, R = 0.24 KJ/kg K

0.21 kg of gas is heated by means of an electric heater for a period of 10 mins during which time the pressure of the gas remains constant. the temperature of the gas is increased from 16⁰C to 78⁰C. the power used by the heater is 20 watts assuming no losses determine

a)the specific heat capacity of the gas at constant pressure

b)the specific heat capacity of the gas at constant volume

c)the characteristic gas constant

d)the density of the gas at a temperature of 160 C and with a pressure of o.12MN/m2

for the gas, take y=1.38