If a sphere hits the floor ~ an acceleration then why does the bounces lower? I typical the energy is passed to the floor then why go the floor give ago less Energy?


*

*

Assuming because that a moment an infinitely hard and also smooth surface, let"s look at the power of the ball.

You are watching: Why does a bouncing ball rise to a lower height with each bounce

When the ball is dropped native a height $h$, initial potential power is $mgh$. Friend would intend it to accelerate to a velocity $v=\sqrt2gh$. However, throughout the fall, it will endure drag from the air. This will reason the dissipation of few of the power of the round into energy of the wait (turbulence, heating, flow). How large this result is will count on the ball, the height, ... For instance a ping pong sphere (light for its size) will suffer a lot greater impact than a golf round (same size, but heavier).

Then we obtain to the impact. The ball will deform throughout the affect - the facility of mass tries to store going, yet the surface ar it hits shot to stop it. This leader to elastic deformation prefer this:

*

The potential energy of the round was convert to elastic energy. You deserve to think of it as the mass of the round being placed to a spring that compresses as soon as you struggle the floor - but there will be some friction (both inside the ball, and specifically between the ball and the floor) which will certainly dissipate energy:

*
.

The picture on the left is the "in flight" state - the feather is uncoiled. The snapshot in the middle is the "fully compressed" state in i m sorry all power of movement would have actually been converted to elastic energy. The photo on the right is the "actual" state: the feather did no compress all the way down because energy to be lost because of friction (and therefore was not obtainable for compressing the spring).

Why carry out I say the friction between ball and floor is important for upright impact? Look in ~ this picture:

*

Image credit: http://deansomerset.com/wp-content/uploads/2011/11/tennis-ball-impact.jpg

This is a tennis ball bouncing top top the ground. See how distorted that is? Imagine taking that spherical surface, and pushing it right into this brand-new shape. The distortion requires you to change the call area. As you do so, sphere rubs against floor. The lateral pressure that this generates dissipates heat - so energy is lost rather of gift stored in the elasticity of the ball.

Of course because that an wait filled ball, there room losses connected with the compression that the air: when the waiting is (adiabatically) compressed, it heats up; while it is hot, that dissipates warm to the environment; and also when it expands, it cools under again. This ought to average that once you hit a sphere it gets cold: but we know that a squash ball, because that example, gets HOT, no cold, as soon as you hit that (this is why squash football player "warm the ball up" prior to playing: as it i do not care hotter, the pressure in the ball rises and it becomes bouncier). This heater is due to the extreme distortion (and for this reason again friction) of the ball during impact:

*
*

Source: screen shots from https://www.youtube.com/watch?v=5IOvqCHTS7o

There are various other loss mechanisms - interior friction that the rubber in the ball, inner friction in the surface you are hitting (sand vs concrete), ...

See more: Driving Distance From College Station To Waco To College Station

All this combine to offer a details ball and also surface combination something called the coefficient of restitution - a number the expresses just how much that the energy of the ball before the impact is "given back" (restitution (noun): the reconstruction of something shed or stolen to its proper owner.) after the impact. This coefficient is constantly less 보다 1 (unless you have actually flubber). Since the height to i m sorry the round will bounce is directly proportional come its energy (barring effects of wait friction), with a coefficient the restitution of much less than one the sphere will bounce less and less high.