Impact Pendulum. Robust is defined as the ability of the assembly to not pop apart (or fail) during operation.

Transcription

1 Imact Pendulum Objectie To construct a endulum deice that will roduce a ti elocity aboe.0 m/s. This should be large enough to ensure that we can break some weak materials. We will then use the endulum to conduct imact tests on three materials and determine the energy required to fail the secimen. This is a task that is commonly erformed, as engineers, to determine the strength of materials. Constraints ) The ti of the endulum needs to be robust enough so that it can withstand imact with arious objects and materials. ) Width of the imact head (the tu) should be narrow ( thin beam width or less). 3) Heay bricks should be close to the imact head. 4) Pendulum suorts (urights) need to be rigid and robust. Your endulum should not break when it imacts an object! 5) Need to minimize tiing of the endulum! obust is defined as the ability of the assembly to not o aart (or fail) during oeration. Construction The imact endulum consists of fie main arts: ) Pendulum arm ) Imact head (the tu) 3) Suorts (urights) 4) Base 5) Secimen mount See the Imact Pendulum Assembly handout for more details on construction. Additional Equiment ) Steel ) Beam balance 3) Carbon aer 4) Meter stick or ruler 5) Protractor 6) Imact materials: notebook aer, aluminum foil, and encil lead.

2 . Physics Concets and Preliminary Measurements Below, you will see the hysics concets necessary to comlete this lab: The Work-Energy Theorem: W r = F d r = KE, KKKK = mm r Angular Velocity with Constant adius: ω = = ti Conseration of inear Momentum: + = +, (for a erfectly elastic collision, the Kinetic Energy is also consered): KKKK cccc + KKKK bbbbbbbb = KKKK cccc + KKKK bbbbbbbb = m You may not hae coered angular elocity or linear momentum in great detail yet, but you will. We will use these concets in a ery basic, straight-forward way to derie exressions for ti elocity and energy loss. We ll discuss these more during the arts of the lab where they are necessary. Note: the unrimed momenta are the momenta before the collision and the rimed momenta are the momenta after the collision. Also, we neglect air resistance throughout this lab. Before we attemt to find the ti elocity of our endulum, we ll need to know a few things first. First, using a rotractor, create a large angle scale to attach to your endulum deice. This will be used to obsere angles during testing. Next, measure the following, using the beam balance and a ruler or meter stick: a) Steel mass m b = kg b) Pendulum arm mass m = kg c) Distance from iot to endulum arm center-of-mass = m d) Pendulum length = m

3 . Energy oss and Ti Velocity First, we will determine how much energy is lost due to friction between the endulum arm and the iot itself and use this to aroximate the ti elocity of the endulum. a) elease the endulum from the horizontal with nothing in the way of the tu. b) Obsere the final angle, θθ, that the endulum arm swings to and record. c) eeat 4 more times and aerage the results (in degrees). Angle θ # Angle θ # Angle θ #3 Angle θ #4 Angle θ #5 Aerage θ d) Determine the amount of energy lost ( E ), using the Work-Energy Theorem, on any gien swing and the energy lost during a 90 swing ( E 90 ). W sinθ = ( m g) dy E = m g m g( sinθ ) E = 0 E = m g sin θ 90 E 90 = E = θ J (In this last equation, we assume that the energy loss due to friction and air resistance is at a constant rate throughout the swing.) 3

4 e) Estimate the ti elocity at the bottom of the swing using the Work-Energy Theorem and the angular elocity exression for circular motion at a constant radius. (Since we hae used EE 90, we assume that the friction force between the endulum and the iot is a constant.) W = ( mg) dy E90 = mg mg( ) E90 = m = g E90 = m / s m ω = = ti ti = = m / s 4

5 3. Projectile Motion, Energy oss, & Ti Velocity Now, let s find the ti elocity another way and erify that we get the same result. This time, let s hae the endulum hit a steel off the table and we ll use the Work-Energy Theorem, conseration of linear momentum for the erfectly elastic collision, the angular elocity exression for circular motion at a constant radius, and rojectile motion to determine ti elocity. a) Place the endulum rig at the edge of the table. b) Place a steel such that the tu will strike it at the bottom of the swing. c) ecord the ertical height from the floor to the osition of the steel. H = m d) elease the endulum arm from the horizontal osition and record where the steel lands using the carbon aer. e) eeat 4 more times and aerage the results (in meters). Distance D # Distance D # Distance D #3 Distance D #4 Distance D #5 Aerage D = m f) et s find the elocity of the steel immediately after the collision using rojectile motion. y( t) = y(0) + y (0) t + ayt 0 = H gt t = H g x( t) = x(0) + x (0) t + axt D = t D = t g = D = m / s H 5

6 g) Estimate the ti elocity at the bottom of the swing before the collision using the Work-Energy Theorem, conseration of momentum for the erfectly elastic collision, the angular elocity exression for circular motion at a constant radius, and rojectile motion. Conseration of Momentum: + = + m = m + mb mb = + m Elastic Collision: KKKK cccc + KKKK bbbbbbbb = KKEE cccc + KKEE bbbbbbbb mm cccc = mm cccc + mm bb bbbbbbbb Combine and sole cccc = mm bb mm bbbbbbbb Plug back into cccc equation cccc = + mm bb mm bbbbbbbb = mm/ss ω = = ti ti = = m / s 6

7 4. Imact Tests Now that we know our assembly works, let s determine how much energy is required to break our imact materials! a) Place material in secimen holder. b) Place secimen holder in base such that the tu will strike the secimen at the bottom of its swing. c) elease the endulum from the horizontal and after it strikes the secimen obsere the final angle, Θ, and record it in the table at the bottom of the age. d) Using the Work-Energy Theorem, let s determine how much energy was required to break the samle. ecord the results at the bottom of the age. e) eeat the aboe stes for the other materials in the table. Θ E = E θ Θ W sin Θ = ( mg) dy Ebreak EΘ = mg mg( sin Θ) Ebreak EΘ = 0 E = m g Θ E break sin Θ Notebook Paer Aluminum Foil Pencil ead Θ = Θ = Θ = E Θ E Θ E Θ E break E break E break 7

8 5. Questions a) If we increased the area of the aer or aluminum foil used when erforming an imact test, would the energy required to break the samle increase or decrease? Why? b) Can we actually assume that the friction force between the endulum arm and the iot is a constant? Why or why not? c) Can we actually assume that the collision between the tu and the steel is elastic? Why or why not? d) Thus, which method of calculating the ti elocity do you think roided a better result? 8