Question #4d466

2 Answers
Aug 2, 2017

Less painfull


As soon as the athlete hits the ground (or cushioned surface), he or she has quite some kinetic energy. This kinetic energy preferably has to be absorbed by the surface. The work the floor does is

#E = (F+F_n)*s#

where E is the energy absorbed by the surface, F is the force that the surface exerts on the athlete to stop him or her, #F_g# is the normal force (constant) to defy gravity and s is the distance the athlete 'falls into the surface'. The amount of energy that the surface has to deliver is fixed, and equal to the kinetic energy of the athlete. One can see now that the higher #s#, the lower #F#. So the softer the surface, the lower the force is that is exerted on the athlete. In other words, it hurts less when the athlete hits the ground, and the stop is less abrupt.

Note 1) #F# is not constant during the stop, but the idea remains the same.

Note 2) The kinetic energy is also partly absorbed by the body, but not not significantly for a soft surface.

Aug 6, 2017

It reduces the impact force on the athlete so that he/she is not injured.


Equation for Newton's second law of motion:
#F = (Δp)/(Δt)#

#Δp# is the impulse (change of momentum). This is equal to the final momentum minus the initial momentum, #Δp = mv - m u#. Initial condition is just before hitting the ground and final is after coming to rest due to collision with the ground.

For a given athlete falling from the bar they've just vaulted over to the ground the impulse is some finite value. The only variables that can be altered are the impact force and the time of collision.

From the above equation impact force and time of collision are inversely proportional.
#F prop 1/(Δt)#

So if the time of collision is small the impact force will be large ⇒ the athlete will be injured! However if the time of collision is large the impact force will be small ⇒ athlete is not injured.

The cushion the athlete lands on increases the time of the collision so that the impact force is reduced to the point that it will not injure the athlete.