Beach Ball
How could a thrown beach ball could cause more harm than a thrown soccer ball. (Kinetic energy?)?
First of all, I must correct: Force = mass x acceleration, not velocity. (Newton's second law).
Suppose a ball with momentum p hits you and bounces off. The impulse (momentum transfer) is 2p, and the average force is approximately the impulse divided by the duration of contact.
While the kinetic energy of a beach ball could in principle exceed that of a soccer ball (newtonian expression for kinetic energy is 1/2 m v^2, for m mass, v velocity), a major obstacle is air resistance.
Air resistance is generally difficult to account for exactly, but two approximations are for low velocity and high velocity (more specifically, Reynolds' numbers). The force due to air resistance can be approximated by:
F = - b v ( low velocity)
F = - a v^2 (high velocity)
Where a and b are constants, largely determined by the object moving. Air resistance is proportional to the cross sectional area of the object. Furthermore, the energy lost per unit time (power) due to air resistance goes like:
P = -(1/2) bv^2 (low velocity)
P = -(1/3) av^3 (high velocity)
For a beach ball to have comparable energy to a soccer ball, because it has much less mass, it must have much higher velocity. The consequence of this is that it loses energy MUCH faster (because the power loss is proportional to the cube of velocity). As a result, beach balls will always slow down much faster than soccer balls. Someone throwing a beach ball with tremendous speed (even as high as 1000 km/hr) at you would not be a great danger (assuming the beach ball were strong enough to not break) because of the energy loss due to air resistance.
However, if the beach ball were thrown at you from a very short distance, it could (in principle) cause more damage than a thrown soccer ball. This is exceedingly improbable, however, because the materials of which beach balls are made are not sufficiently resilient to apply much force.
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 Octopus Has my Beach Ball Funny picture 18mm link charm US $5.50 |
 VINTAGE Photo L5799 Woman on rock with beach ballocean US $5.98 |
 New MIB Hannah Montana Beach Ball Swim Raft Lot US $9.99 |
 BEACH BALL Key Fob really cute keychain US $7.00 |
 14G Green Purple Beach Ball Belly Navel Ring US $2.00 |
 NH HAMPTON BEACH NEW HAMPSHIRE 1948 Postcard CASINO BALL ROOM US $4.50 |
 10 Disney Tinkerbell Party Favors 20 Pool Beach Balls US $19.95 |
 CELTIC VIEW DONT FORGET YOUR BEACHBALL May 14 2003 Vol 38 43 US $9.47 |
 Disney Tinkerbell Swim Ring Tube Float Pool Beach Ball US $9.95 |
 Coney Island Beach Ball Players 1800s 4x6 Reprint Of Old Photo US $7.99 |
 Lot of 6 White GRADUATION Class 2012 PARTY AUTOGRAPH Beach BALL Favor Keepsake US $5.99 |
 smile face beach ball 7 inch size and 12 smile face tattoos party favors z US $5.00 |
 VINTAGE Photo L5751 Man sitting by beach ball US $5.98 |
 NEW HUGE SPLASH INFLATEABLE BEACH BALL play toy 48 IN US $6.64 |
 2 NEW HUGE SPLASH INFLATEABLE BEACH BALL play toy 48 IN US $12.34 |
 inflatable beach ball 10 inch american flag design patriotic rwb US $5.50 |
 Vintage sterling silver CIRCUS ISLAND BEACH SEAL PLAYING w ENAMEL BALL charm US $9.97 |
 New Finding Nemo 20 in Beach Ball and Swimmies US $15.99 |
 70S ORANGE BARBIE POOL SET LOUNGE CHAIR FLOATERSBEACH BALLLONG FLOATERS US $9.97 |
 Silver Enamel 3D Beach Ball Charm a Brighton Jewelry Tin or FREE Ship US $12.34 |
 NOS TEDDY RUXPIN CASSETTE TAPE GREATEST HITS BEACH BALL US $10.50 |
 1992 US OPEN GOLF BALL MARKER AT PEBBLE BEACH CC LQQK RARE US $12.95 |
 NWT Vintage Front Peace Patch Adjustable Trucker Hat Beach Mesh Ball Cap US $11.99 |
 NWT Adjustable Vintage Iowa Patch Trucker Hat Beach Mesh Ball Cap Black US $11.99 |
 NWT Adjustable Vintage Iowa Patch Trucker Hat Beach Mesh Ball Cap Camo US $11.99 |
 NWT Adjustable Vintage Iowa Patch Trucker Hat Beach Mesh Ball Cap Red US $11.99 |
 NWT Adjustable Vintage Patch Trucker Hat Beach Mesh Ball Cap Black White US $11.99 |
 NWT Adjustable Trucker Printed Hat Beach Mesh Ball Cap GreenBlueWhite US $11.99 |
 Mount Gay Rum Beach Ball US $5.00 |
 A 1939 KESTOS BEACH SWIM SUIT FASHION OCEAN BALL SAND AD US $21.95 |
 Siamese Cat Ocean Sand Beach Ball FuN ArT by BiHrLe Print 5x7 US $15.00 |
 Model With Beach Ball Vintage 8x10 Reprint Of Old Photo US $12.99 |
 14G Tongue Barbell Rings Iridescent Beach Ball Lot of 5 US $4.25 |
 A 1934 VALLEE SEMI NUDE PINT UP WOMAN BEACH BALL SPORT OUTDOOR ART DECO STYLE AD US $21.95 |
 NEW Marvel Spider Man Beach BallAge 3Toys US $5.50 |
 Disney Pixar Cars Beach Ball NEW Age 3Toys US $5.50 |
 INFLATABLE THE AMAZING SPIDER MAN BEACH BALL BEACHBALLS US $7.49 |
 Beach Ball Charm Fit BraceletEUROPEAN Bail US $2.99 |
 Becky Sharp Beach Ball PICTURE Trade Tour Promo AD US $3.95 |
 6 Inflatable YELLOW DUCK Ducky BEACH BALLS 10 party favors FREE S H ducks beach US $12.95 |
 6 INFLATABLE GEOMETRIC PATTERN BEACH BALLS 7 FREE S H party favors beach pool US $8.95 |
 BEACH BALL Light Set hawaiian luau party FREE SHIP pool beach party US $12.95 |
 6 INFLATABLE PATRIOTIC STARS BEACH BALLS 7 July 4th FREE S H red white blue US $8.95 |
 6 INFLATABLE SPRING COLORS BEACH BALLS 7 FREE S H party favors pool US $8.95 |
 6 Inflatable LADYBUG BEACH BALLS 14 party favors FREE S H lady bugs pool beach US $11.95 |
 6 INFLATABLE Mini BLUE POLKA DOT BEACH BALLS 7 polka dots FREE S H pool beach US $8.95 |
 6 INFLATABLE USA STARS and STRIPES BEACH BALLS 7 FREE S H July 4th party favors US $8.95 |
 NEW 6 PC POOL TOYS Beach Ball Innertube Swimming EK SUCCESS 3D Stickers NIP US $3.29 |
 LOGO GOLF BALL PEBBLE BEACH GOLF LINKSBLACK TEXTCALIFORNIA US $1.99 |
 LOGO GOLF BALL SPYGLASS HILL GOLF CLUBPEBBLE BEACH CA GREEN TEXTPROV1 US $2.99 |
 LOGO GOLF BALL SPYGLASS HILL GOLF CLUBPEBBLE BEACH CA GREEN TEXT US $6.99 |
 LOGO GOLF BALL PEBBLE BEACH GOLF LINKSCIRCLE LOGOCALIFORNIA US $9.99 |
 LOGO GOLF BALL POPPY HILLS GOLF CLUBPEBBLE BEACH CA ATT PB PRO AM2 LOGOS US $9.29 |
 LOGO GOLF BALL PEBBLE BEACH GOLF LINKSBLUE GREEN TEXTCALIFORNIA US $6.50 |
 Beach Diva Applique Blue Swim Cap With Flowers Born To Surf Tatoo Beach Ball US $2.99 |
 Pink and White Beach Ball US $1.29 |
 Beach Diva Applique Beach Umbrella Bag Towel Ball Blue Flower Innertube US $2.99 |
 Pirate Beach Ball US $1.49 |
 NEW Disney Pixar Cars Swim Ring 21 and Beach Ball Combo Set Ages 5 McQueen BOX US $12.99 |
 NEW Disney Pixar Cars Swim Raft 45 and Beach Ball Combo Set Ages 5 McQueen BOX US $12.99 |
 Three Bud Light Beer Foot Ball Beach Lounge Stadium Chairs US $34.99 |
 Sugarn Cream Cotton Mill End Yarn Color BEACH BALL BLUE One Pound Four Ply US $8.19 |
 Vintage 1996 University of Washington Holiday Bowl Husky Beach Ball Button US $8.00 |
 1 BEACH BALL Inflate Approx14 when Inflated New FREE USA SHIPPING US $3.99 |
 NY YANKEES BEACH BALL 24 MLB 0059 706 OFFICIALLY LICENSE BRAND NEW US $9.99 |
 12 BEACH BALLS Approx14 when Inflated New FREE USA SHIPPING US $16.99 |
 Play Beach Ball Seagull Garden Decor stands 12 1 2 in tall New HURRY PRICE DROP US $9.99 |
 Blue Glitter Ball Gearstick Premium Shift Gear Knob VW Beach Buggy T1 Beetle T2 US $33.99 |
 White Beach Wedding dress Quinceanera party Prom Cocktail Evening Ball gowns New US $156.00 |
 25 Assorted BEACH BALLS Approx14 when Inflated New FREE USA SHIPPING US $29.99 |
 3 inflatable 16 inch beach balls luau pool party 6 color heavy vinyl US $17.00 |
 Green Glitter Ball Gearstick Premium Shift Gear Knob VW Beach Buggy T1 Beetle T2 US $33.99 |
 3 inflatable beach balls 10 inch american flag design patriotic rwb US $12.00 |
 Savvy Tabby Rattle N Roll Beach Ball Cat Toy US $2.99 |
 w Swarovski Crystal Ball Drop Ocean Beach Bridal Wedding Sterling Silver ANKLET US $68.00 |
 2 INFLATABLE 12 SMILE FACE BEACH BALL YELLOW US $1.49 |
 Volleyball players Beach sand sun net ball fabric 1y sewing Wilmington US $9.99 |
 8 UV Beach Balls Belly Button Ring Navel 14 Gauge BY3 US $6.98 |
 1940S PALM BEACH FL BREAKERS BALL ROOM PHOTO POSTCARD US $9.99 |
 Beach Wedding fashion Women bridal Strapless Deep V Ball Prom Dress bridesmaids US $108.00 |
 12 Wedding Beach Balls Decorations favors Bridal Shower Anniversary 25th Dance US $9.99 |
 GO DIEGO GO BEACH BALL 20 INFLATABLE WATER TOY US $4.99 |
 DISNEY PRINCESS BEACH BALL THE LITTLE MERMAID INFLATABLE WATER TOY US $4.99 |
 DORA THE EXPLORER BEACH BALL 20 INFLATABLE WATER TOY US $4.99 |
 DISNEY 2006 HIDDEN MICKEY Cast Lanyard Beach Ball Collection Clarabelle PIN US $1.99 |
 MLB0059 703 24 Beach Ball Chicago Cubs US $22.53 |
 MLB0059 705 24 Beach Ball NY Mets US $22.83 |
 MLB0059 712 24 Beach Ball Chicago White Sox US $21.93 |
 MLB0059 724 24 Beach Ball Detroit Tigers US $24.69 |
 MLB0059 719 24 Beach Ball Angels US $22.14 |
 MLB0059 714 24 Beach Ball Cincinnati Reds US $23.58 |
 CLG0059 625 24 Beach Ball Virginia Tech US $22.83 |
 CLG0059 637 24 Beach Ball U of Maryland US $25.52 |
 CLG0059 604 24 Beach Ball University of Texas at Austin US $22.48 |
 CLG0059 644 24 Beach Ball Texas AM U US $24.74 |
 CLG0059 649 24 Beach Ball West Virginia U US $24.74 |
 CLG0059 607 24 Beach Ball University of Georgia US $24.74 |
 CLG0059 654 24 Beach Ball Indiana US $22.32 |
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