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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 Shore Sandpipers At The Beach Bath Accessories Bathroom Collection Choice US $21.99 |
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 GOEBEL HUMMEL BEACHBALL BABY US $60.00 |
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 VOLLEYBALL 1 BEACH VOLLEY BALL GRAPHIC DECAL STICKER US $3.28 |
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 Postcard Interior Ball Room Redondo Beach Auditorium CA US $9.99 |
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