Final Review #4 Experiments Statistical Mechanics,Kinetic TheoryIdeal Gas ThermodynamicsHeat EnginesRelativity 8.01t December 8, 2004Review of 8.01T ExperimentsReview of 8.01T ExperimentsDataStudioExperiment 01: Introduction toExperiment 01: Introduction to DataStudioPosition of hand motion Where is the velocity zero? Where does the magnitude of the velocity reach its maximum?Experiment 02: Projectile MotionExperiment 02: Projectile MotionReminder on projectile motion Horizontal motion (x) has no acceleration. Vertical motion (y) has acceleration –g. Horizontal and vertical motion may be treated separately and the results combined to find, for example, the trajectory or path. Use the kinematic equations for x and y motion:Experimental setup Coordinate system Impact point: ¾ Height: h ¾ Horizontal displacement: r With chosen coordinate system: ¾ ¾ Horizontal displacement: x=r Solve above equation for g: Theta θ>0: upward Theta θ<0: downward Height: y=-hExperiment 03: Modeling ForcesExperiment 03: Modeling ForcesExperimental setup h Measuring the magnet gap h2- Measure heights h1 and h2 1 with your ruler, and subtract them. (h1 will be constant.) The two magnets stuck together weigh 6.0 pennies. The plastic coin holder weighs 4.0 pennies. Enter the gap (in mm) and the total weight (in pennies) into a table in DataStudio. The gap goes in the X (left) column of the table.Exponential fit Carry out a user-defined fit of: Record A and C for part (a) and answer question about the characteristic length l over which the force drops by a factor 1/eSemi-log plot and linear fit IIExperiment 04: Uniform Circular MotionExperiment 04: Uniform Circular MotionGoal produce a centripetal acceleration Study a conical pendulum and measure the force required to Extract from measurement of angular frequency and rm the spring constant k and pre-tension F0 Understand how an instability in this system occurs at a critical frequency ω0 and how to extract ω0 from your measurementsAnalysis of conical pendulum F s From my measurements of rm, ω: θ≈88° Therefore: Ignore effect of gravitation!Fitting Perform a User-Defined fit to: A/(1-x*x/(B*B))Experiment 05A: Static equilibriumExperiment 05A: Static equilibriumxGoal When a weight is suspended by two strings in the center as shown in the photograph below, the tension is given as follows: θθH x T Mg θθT GoalGoal: Measure T for several values of θ using measurements of , H (fixed), to verify the equation above!Analyzing data Calculate sinθ from your vertical drop measurements (see write up). Plot force on y axis, sinθ on x axis. Fit y = A/x (User-defined fit) to your data.Experiment 06: Work, Energy and the Harmonic OscillatorExperiment 06: Work, Energy and the Harmonic OscillatorEquipment setup Use the heavy spring on the force sensor. Put two 250g weights in the cart. Clip motion sensor to other end of track, and support it on a piece of 2x4.Measurement Results Position vs. Time: Measure maximum heights either side of 2nd bounce, calculate loss of potential energy, and friction force. Enter in table! Force vs. Time: Expand force peak around 2nd bounce.Finding Acceleration Up & Down Linear fit to find aup Linear fit to find adownCollisionsExperiment 07: Momentum andExperiment 07: Momentum and CollisionsEquipment setup Use the lighter spring on the force sensor. Clip the motion sensor to the end of the track. Level the track. Place Target cartTarget cartat rest about 10cm from the spring10cm from the spring. Place Incident cartIncident cartabout 1616--20cm from motion sensor20cm from motion sensor. Note: Velcro facing = inelasticVelcro facing = inelasticand magnets facing = elasticmagnets facing = elastic. Roll incident cart just hard enough to come back to its starting point. Practice this first before you take your data!Practice this first before you take your data! Make measurements with different weights of incident and target cart.Graph 1 Two equal mass carts A and B collide. This is XA vs. time. 1. Along line AB? 2. At point B? 3. Along line BC? 4. At point C? 5. Along line CD? At approximately what time does cart B hit the spring?Graph 2 Two equal mass carts A and B collide. This is VA vs. time. 1. Along line AB? 2. Along line BC? 4. Along line DE? 3. Along line CD? 5. Along line EF?Graph 3 A cart of mass 0.25kg collides with a spring on the force sensor. Here is the force during the collision. The fit is to: A*sin(2π(x-C)/T) What does the area under the curve tell you? What can you learn from the parameter T?Experiment 08: Physical PendulumExperiment 08: Physical PendulumGoals Investigate the oscillation of a real (physical) pendulum and compare to an ideal (point mass) pendulum. Angular frequency calculation: Practice calculating moments of inertia, using them, and solving the τ = I a equation of motion.Understanding the graphs Position vs. time data from the motion sensor. What is happening: 1. Along the top plateaus marked by A? 2. At the downward peaks marked by B? How do you use this graph to find the period of oscillation of the pendulum?Experiment 09: Angular momentumExperiment 09: Angular momentumMeasure rotor IR Plot only the generator voltage for rest of experiment. Use a 55 gm weight to accelerate the rotor. Settings: ¾ Sensitivity: Low ¾ Sample rate 500 Hz. ¾ Delayed start: None ¾ Auto Stop: 4 seconds Start DataStudio and let the weight drop.Understand graph output to measure IR Generator voltage while measuring I .What is happening:R1. Along line A-B ? 2. At point B ? 3. Along line B-C ? How do you use this graph to find IR ?Measure IR results Measure and record αup and αdown. For your report, calculate IR:transformationExperiment 10: EnergyExperiment 10: Energy transformationEquipment setup Digital Volt Meter Mechanical equivalent to heat: A motor applies a known friction jar with a known mass of H2O. Electrical equivalent to heat: Apply voltage (2.5V) across a resistor (2.5Ohms) and use resulting electrical heat: Resistor is connected to right pair of posts. How can one double the temperature increase in both setups for a fixed amount of time? torque τf at a known ω to a plastic c = τfω ( ) c = ∆VI ( ) mdT dt mdT dtREVIEW #4 Statistical Mechanics, Kinetic Theory Ideal Gas Thermodynamics
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