Mechanical Equivalent of Heat Data, Analysis 81 Questions Sheet Physics 231 Name: Date: Mass of Primary Weight [weight of bucket + 5kgl mH Mass of Counterwei -, ht mG Mass of Aluminum cylinder Diameter of cylinder where friction occurs DR Ambient Temperature Initial Temperature of Cylinder Ti Final Temperature of Cylinder Initial Resistance Hi I Final Resistance Rf I Analysis and Questions: 1. Conversion of mechanical work into heat 3. Experiment procedure i. First the various masses are measured: I Primary weight {e.g. bucket with water} in... I Counterweight {attached to friction cord] mg I Aluminum cylinder m=0.249 kg ii. Dthervalues to be measured in advance: I Ambient temperature Tu I Diameter of cylinder where friction occurs DR: 45.?5 mm iii. After cooling the cylinder, it should be screwed to the base, the temperature sensor should be inserted and the friction cord should be wrapped around it. {See image above}. iv. After a few minutes, that should be ignored for the sake of a homogenous temperature distribution, the resistance of the temperature sensor is R1 = 3.00 k0 [corresponding to T1 = 14.60\"\": by Eq. 1]. v. After zeroing the counter, the experiment is begun by turning the crank and thus lifting the primary weight from the ground. This slightly loosens the cord so that it causes less friction on the cylinder. The primary weight now remains at the same height and should remain there forthe rest ofthe experiment. vi. After :1 = 451] turns the experiment is halted and the resistance value read off: {for example: HZ = 3.99 kn [72 = 30.26 C]l. Since the temperature continues to rise for a short time after the experiment is completed [homogenizing the temperature distribution}, the minimum value of the resistance is noted as the measured value. This is reached a few seconds after the end ofthe experiment. After that the resistance increases again since heat is exchanged with the environment to cool the cylinder down to a lower temperature. Mechanical Equivalent of Heat - Data, Analysis & Questions Sheet Physics 231 Name: Date: b. Experiment evaluation . Work W is defined as the product of force F and displacement s W = Fs (2) . The force of friction acting is F = mA g(3) (g is the acceleration due to gravity) in the direction of the displacement 5 = nnDr(4) . Placing Equations 3 and 4 into Equation 2 gives: W = mAgnnDR = 5.22 x 9.81x 460 x 3.1416 x 0.04575 Nm = 3386 Nm (5) The heat stored in the friction cylinder AQ is determined from the temperature difference (72-71) and the specific heat capacity given in Section 2: AQ = CAmA (T2- T1) = 0.86 x 0.249 x (30.26 - 14.60) kJ = 3353 J (6) . In this example the disagreement between the mechanical work and the heat energy is found to be no more than about 1%. Due to unavoidable tolerances relating to the composition of materials (aluminum is very soft and almost impossible to work mechanically, so that it is always alloyed), the specific heat capacity can fluctuate quite noticeably.3. If it is observed that the cord moves to the right when the crank is turned or fails to remain in its groove, then the cord should be wrapped around the cylinder so that the and of the cord with the weight is on the right and that with the counterweight is on the loft. 4. The temperature sensor should be watted with a drop of oil [importantly and inserted into the selected friction cylinder according to Fig. 1 [this should have already bean done for you) until it is felt to snap into place and can be turned easily [if it is inserted too far or not far anough, it is not easy to turn it). The two connections of the temperature sensor are attached to a resistance meter [multimeter) operating in the range 2 kQ to $ 10 with a display accurate to at least three figures. The conversion of the resistance measured into a comresponding temperature can be performed either with the help of the conversion table on the last page of these instructions or by using the following equation T - (217/R ]- 151[1) where? must be given in ko to obtain Tin "C. This equation agrees with the table provided by the NTC thanmistor manufacturer in the range from 10 - 40 "Cto an accuracy of approximately + 0.05 "C ""OPTIONAL STEP - ank instructor before doing"" Before an experiment the friction cylinder can be cooled to about 5 - 10"C below the ambient temperature. This can be achieved by putting it in a plastic baggie and sitting it on ice. The hole for the temperature censor should point upwards and the cylinder may only be submerged in ice to a depth of about 2/3 the height of the cylinder. The plastic baggy should keep the cylinder from weding dried off. The rise in temperature during an experiment should continue until the friction cylinder's Commporabure has been raised to about 5 - 10"C above the ambient temperature. The more preckely the temperature differences for cooling and hosting (with respect to the ambient temperature] are similar, than the smaller is the nat exchange of heat with the environment Setup: 1. Plug the black banana cord into the COM port on the Multi-meter, and the red banana cods into the right most red port. Than plug both cords into either port on the temperature sensor. Tum the multi-meter on and make sure the dial is set to Joke 2. Weigh the various massas: a. Primary weight (weight of the bucket + 5kg] mH b. Counterweight (black cylinder attached to friction cord) mG c. g Aluminum cylinder MA = 0.249kg 3. Place the bucket on the floor and carefully place the Sky weight into the bucket. 4. Wrap the friction cond from right to left and front to back with the bucket and at the right-front side of the groove in the aluminum cylinder. See picture below. U1030's Equivalent of Hest Apparatus 1 2 3 4 1. Base with conversion table with rethinke -> temperature S. Capper cylinder (U30465. not Included) 4. Bectrical heating element 5. Hand crank & Table dump 7, Friction good with counter weight [not show 9. Temperature sumer 10, Adaptorcable LL. Bucket SL. [not showry 10 Procedure:" "READ THE ENTIRE PROCEDURE BEFORE YOU START" " 1. Other measurements needed: a. Ambient temperature TU [use thermometer to measure current temperature) b. Diameter of aluminum cylinder where friction occurs OR = 45.75 mm c. The resistance of thecylinder before starting should be - 8.00 big. = R (comesponding to 7, = 14.60"C in Eq. 1) 2. If the resistance of the cylinder before starting isn't - 8.00 ko, notify your instructor and get guidance from them on cooling your cylinder if needed. 3. After zeroing the counter, bagin turning the crank quickly and steadily, [this should lift the bucket slightly off the ground and maintain that height through the procedure ) 4. Stop turning the crank once the counter hits 460 turns and gently lower tha bucket to the floor. (Letting the bucket drop to the floor will damage the bucket ) Since that resistance still drops some after the procedure ands you should wait till it starts to rise and record its minimum value as Ry in the chart below. (R) = 3.99 ko [T; - 30.26 "C)