Quiz #1 Solution

ME231C Quiz 1 Question # 1 (10): Gravity decreases with altitude, since greater altitude means greater distance from the Earth's centre. If someone climbs to the top of Mt. Everest, he/she will be about 5.5 mile above sea level where the acceleration of gravity is 32.09 ft/s2. If a person whose weight is 200 lbf in Ames where acceleration of gravity is 32.2 ft/s2 climbs to the top of Mt. Everest, what would be his weight? What is the mass of the person? Neglect all other variations. Acceleration of gravity on Everest 232.09 /Eg ft s= Acceleration of gravity at Ames 232.2 /Ag ft s= Weight in Ames 200AF lbf= Find: Weight on Everest, EF Mass of the person, m Solution: Relevant equation: . E A E A F FFF m g m g g g= ? = = = Rearranging: ( ) 2 2 32.09 / 200 199.317 32.2 / E E A A g ft sF F = lbf = lbf g ft s ? ?= ? ?? ? 2 2 200 32.2 . / 200 32.2 / 1 A A F lbf lb ft sm lb g ft s lbf= = = Question # 2 (6): During a process, the temperature of a system rises by 100°C. What would be the rise in temperature in K, °F, and °R? Relevant equation: ( ) ( ) ( ) ( ) ( ) ( )1.8O O O O OT K T C T F T C T R T F? = ? ? = ? ? = ? ( ) 100T K K? = ( ) 180O OT F F? = ( ) 180O OT R R? = Note: Some of you used Slug as a unit of mass. It is not incorrect; however I prefer using kg and lb mass in this course. Note: The question is asking for equivalent rise in temperature (change in temperature) in K, °F, and °R scales, not to convert 100°C in those units. ME231C Quiz 1 Question # 3 (10): Air contained within a piston-cylinder assembly is slowly heated. As shown in Figure, during this process the pressure first varies linearly with volume and then remains constant. Determine the total work, in kJ. Expansion work 2 1 V V W p dV= ? ( ) ( )( ) 231 212 2 1 1 / 175 2 1502 1 1 .p p kN m kJW V V kPa m kJkPa kN m+? ?= ? = =? ?? ? ( )( ) ( )( ) 2323 2 3 2 1 / 1100 2 2001 1 .kN m kJW p V V kPa m kJkPa kN m= ? = = 12 23 150 200 350TotalW W W kJ kJ kJ= + = + = State Volume, m3 Pressure, kPa 1 1 50 2 3 100 3 5 100 1 2 3 meisu Microsoft Word - Quiz 1_Solutions.doc