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Physics 199BB The Physics of Baseball

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Physics 199BB The Physics of Baseball

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    1. Week 2 1 Physics 199BB The Physics of Baseball Fall 2007 Freshman Discovery Course Alan M. Nathan 403 Loomis 333-0965 a-nathan@uiuc.edu Week 2

    2. Week 2 2

    3. Week 2 3 Position, Velocity, and Acceleration Position: x,y,z Units of length (m, ft, …) Trajectory completely known if we know the position of an object at every instant of time x(t),y(t),z(t) Position is a vector with three components

    4. Week 2 4 Position, Velocity, and Acceleration 2. Velocity vx,vy,vz Units of length/time (m/s, ft/s,mph,…) Velocity is the rate of change of position Velocity is a vector with three components

    5. Week 2 5 Position, Velocity, and Acceleration 3. Acceleration ax,ay,az Units of length/time2 (m/s2, ft/s2,…) Acceleration is the rate of change of velocity Acceleration is a vector with three components

    6. Week 2 6 Motion with Constant Acceleration x = x0 + v0t + ˝at2 v = v0 + at

    7. Week 2 7 Special Case 2: Two-dimensional projectile motion with gravity x = x0 + v0xt vx = vx0 (constant) y = y0 + v0yt - ˝gt2 vy = v0y - gt

    8. Week 2 8 Detailed example: pitched baseball Suppose a pitcher throws a baseball with an initial horizontal velocity of 90 mph at a height of 6 ft above home plate. How long does the pitch take to reach home plate? How much does the pitch drop vertically?

    9. Week 2 9

    10. Week 2 10 Useful thing to remember To convert mph to ft/s, multiply by 1.467 To convert ft/s to mph, divide by 1.467

    11. Week 2 11

    12. Week 2 12 Using Excel to Compute the Trajectory divide up time into slices separate by dt suppose x,y,vx,vy are known at time t at time t+dt x(t+dt)=x(t)+vx(t)*dt y(t+dt)=y(t)+vy(t)*dt vx(t+dt)=vx(t)+ax(t)*dt vy(t+dt)=vy(t)+ay(t)*dt for case at hand values known at t=0: x0,y0,v0x,v0y ax=0 ay=-g

    13. Week 2 13 Detailed example: batted baseball Suppose the baseball is hit at an initial height of 3 ft off the ground at a speed of 100 mph and an angle of 35o to the horizontal. How far does it travel? How long is it in the air? How high does it go?

    14. Week 2 14 Detailed example: batted baseball Suppose the baseball is hit at an initial height of 3 ft off the ground at a speed of 100 mph and an angle of 35o to the horizontal.

    15. Week 2 15 Batted Ball Example x = x0 + v0xt = x0 + v0tcos(?) y = y0 + v0tsin(?) - ˝gt2 x0=0 y0=3 ft v0=146.7 ft/s ?=35o

    16. Week 2 16 Batted Ball Example x = x0 + v0xt = x0 + v0tcos(?) y = y0 + v0tsin(?) - ˝gt2 x0=0 y0=3 ft v0=146.7 ft/s ?=35o

    17. Week 2 17 Batted Ball Example x = x0 + v0xt = x0 + v0tcos(?) y = y0 + v0tsin(?) - ˝gt2 x0=0 y0=3 ft v0=146.7 ft/s ?=35o

    18. Week 2 18 Now let’s use Excel to solve (just like before) divide up time into slices separate by dt dt needs to be “small” suppose x,y,vx,vy are known at time t at time t+dt x(t+dt)=x(t)+vx(t)*dt y(t+dt)=y(t)+vy(t)*dt vx(t+dt)=vx(t)+ax(t)*dt vy(t+dt)=vy(t)+ay(t)*dt for case at hand values known at t=0: x0,y0,v0x,v0y ax=0 ay=-g

    19. Week 2 19 Some Useful Formulas (we won’t use these for anything) Maximum distance D = v02sin(2?)/g Maximum height H = v02sin2(?)/2g Time of flight T = 2v0sin(?)/g D is largest when ?=45o T and H are largest with ?=90o

    20. Week 2 20 Baseball Trajectories with Drag and Magnus Forces Some additional physics concepts Newton’s First Law Objects at rest stay at rest and objects in motion continue to move at constant velocity if not acted upon by an external force In other words, with no external force v is constant in both magnitude and direction Newton’s Second Law Forces cause acceleration: a = F/m or

    21. Week 2 21 Forces on a Baseball in Flight Gravity Already discussed Drag (“air resistance”) Force We will do this next Magnus Force We will do this later Direction of Fd and Fl. Demo with styrofoam ball. Direction of Fd and Fl. Demo with styrofoam ball.

    22. Week 2 22 Baseball Trajectories with Drag Fdrag= ˝ CD?Av2 ? is density of air 1.23 kg/m3 at normal temp and pressure A is cross sectional area of ball A = ?R2 = 4.16 x 10-3 m2 v = speed of ball CD is drag coefficient A number between 0 and 1 Approximately 0.5 for v<50 mph See plot in Adair, p. 8, Fig. 2.1 Direction of force is exactly opposite velocity Direction of Fd and Fl. Demo with styrofoam ball. Direction of Fd and Fl. Demo with styrofoam ball.

    23. Week 2 23 Drag Coefficient from Adair

    24. Week 2 24 Let’s estimate size of drag force Let CD = ˝, v=100 mph FD = ˝CD?Av2 Convert mph to m/s: 100 mph = 44.7 m/s FD=1/2*1/2*1.23*4.16x10-3*(44.7)2 FD = 2.56 N = 0.574 lb By comparison, weight of ball is 5.1 oz mg = 0.319 lb We conclude that the drag is very important

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