Structural Steel DesignSolve the following three problems. Please show all your work.
Lab 7: CollisionsIn the PhET simulations, choose “Collision Lab”. If you can open it, fine. On my computer, theonly way I could open it was to click on “Collision Lab HTML5”, below the download button.Here’s a link:https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab_all.htmlNext, choose “Explore 2D”. You’ll use “Explore 2D” for both parts of the experiment.Part 1: Conceptual, Tracking the Center of Mass (CM)On the right hand side, check Center of Mass, Reflecting Border, and Path. (Uncheck theothers).Also on the right hand side, make sure the elasticity is at 100% (in other words, elastic collisionswith no loss of kinetic energy from the system.)Between the main rectangle and the right hand side, choose the number of balls to be 2.On the bottom, choose mass 1 = 0.50 kg, mass 2 = 1.50 kg.Also on the bottom, you can choose “normal” or “slow” for the speed. I had the best luck withusing normal some of the time, but then changing to slow just before collisions, so I couldobserve the collision more closely.Use this equation as a reference:(eq. 1) ΣF (Σm) (a )external = CM sysIn words, the total external force on a system equals the total mass of the system times theacceleration of the center of mass of the system.The “x” in the diagram is the center of mass of the system.Run the simulation and watch it for a while while the balls bounce off the walls and off eachother, paying special attention to the behavior of the center of mass (CM). Then answer thequestions below:a) When one of the balls bounces off a wall, what happens to the direction of the velocityof the CM? ____________________ (does it stay the same or does it change?)b) Keeping in mind that the “system” consists of the two balls, and referring to equation1 as needed, explain why the direction of the CM does what you said in (a) above. (Hint:think of whether forces are internal or external to the system.)(see next page)Before answering (c) and (d) below, make sure you have observed the behavior of the CMduring a period of time when the balls bounce off each other but neither one bounces off a wall.It might take a couple minutes of observing to see this, and remember you can slow it down justbefore they hit each other so you have more time to observe the CM during the collision.c) When the balls bounce off each other, and neither ball is bouncing off a wall, whathappens to the direction of the velocity of the CM? ____________________(does it stay the same or does it change?)d) Keeping in mind that the “system” consists of the two balls, and referring to equation1 as needed, explain why the direction of the CM does what you said in (c) above. (Hint:think of whether forces are internal or external to the system.)Part 2: Numerical, checking conservation of momentumStay in the “Explore 2D” part and use the following settings:On the right hand side, check “Values” and “Reflecting Border”. Uncheck all the others.Elasticity will still be 100%.Number of balls will still be 2.Mass values will still be mass 1 = 0.50 kg and mass 2 = 1.50 kgNear the lower left corner, check “More Data.” In the data table that opens up, the only valuesyou’ll use will be the components of momentum (p and p ) and the mass values. x yNow run the simulation. Wait until you can get a clean collision of the two balls without thecomplication of either ball hitting a wall. Stop the motion just before the collision and fill in theinitial values for all of the following:p 1x, p 1y, p 2x, p 2y(in first data table on following page ), and speed |v and speed (in | 1||v|| 2||second data table). You can either get the speeds by reading them off the picture (they shouldbe close to each ball in the picture), or by using Pythagorean’s theorem on the x and ycomponents of each velocity.At this point you should have filled in 4 cells in the first data table below, and 2 cells in thesecond data table.Now briefly start the simulation again, then stop it right after the collision. (It doesn’t matter ifthere’s a little lag time, as long as neither ball hits a wall.) Now fill in the final values of the same6 quantities you just did.In the first data table, get the initial ( p ) value by adding and . Get the final ( x sys p 1x p 2x p )x sysvalue the same way. Then get the ( py) sys values by adding the individual y components of themomentum.e) Are the initial and final ( p ) values within 2% of each other? _ (yes or x sysno). If not, track down any calculation errors, or re-do the simulation.f) Are the initial and final ( p ) values within 2% of each other? _ (yes or y sysno). If not, track down any calculation errors, or re-do the simulation.In the second data table, use the formula K = 1/2 * m * |v| to calculate and before2 K1 K2and after the collision. Calculate the initial and final K sys by adding K and . 1 K2g) Are the initial and final K sys values within 2% of each other? _ (yes orno). If not, track down any calculation errors, or re-do the simulation. The initial and final Ksysvalues are theoretically the same, because the collision is elastic.(All cells have units of kg · m/s)m 1 = _ kgm 2 = __ kg(m/s) (m/s) (J) (J) (J)p 1xp 1y p 2x p 2y( p )x sys ( p )y sysInitialFinalspeed v|| 1||speed v|| 2||K 1 K 2 K sysInitialFinal
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