f=ma wrote:
Your mass and the acceleration of gravity remain constant. That's why the force returned from any given running surface (assuming flat terrain) remains the same as the force applied at toe off.
I think this and part of what rekrunner said makes the most sense to me.
RyecorDone wrote:
Newton's 3rd law applies imperfectly for real world running because it's not a "perfectly elastic" impact. If your body was perfectly rigid and hit a perfectly rigid surface, then the law would work. We're not billiard balls bouncing off of slate..
There is no requirement for elastic impact (or any impact) in Newton’s third law. If I push against a wall I feel the wall pushing back. If I push against a cart the cart moves, but I still feel the cart pushing back.
If I drop a billiard ball in water the ball applies force to the water causing waves. The water applies force to the ball causing it to slow down.
Paul2432 wrote:
RyecorDone wrote:
Newton's 3rd law applies imperfectly for real world running because it's not a "perfectly elastic" impact. If your body was perfectly rigid and hit a perfectly rigid surface, then the law would work. We're not billiard balls bouncing off of slate..
There is no requirement for elastic impact (or any impact) in Newton’s third law. If I push against a wall I feel the wall pushing back. If I push against a cart the cart moves, but I still feel the cart pushing back.
If I drop a billiard ball in water the ball applies force to the water causing waves. The water applies force to the ball causing it to slow down.
Exactly. I think I should have originally just asked if I dropped a brick on grass or pavement how things are different.
I'll chime in, considering I have a degree in physics. I think RyecorDone is thinking in the right direction.
There is more going on here than just newton's third law. Because you are dealing with deformable objects (soft turf) you need some more concepts to understand what is happening. Newton's laws only strictly apply to rigid body (non-deformable, forces only acting on points and lever arms) mechanics, and apply to other scenarios only in an approximate way. All the 'laws' of physics are ultimately models with various assumptions about reality.
It's better to think about what's going on here with energy/thermal physics instead of only newton's laws. You are losing energy on the soft surface because you are spending it increasing the entropy of the surface as it's deforming. What this means is that the forces that the ground is applying to you are smaller (which is really what makes you move, think about running in the deep end of a swimming pool--you don't really go anywhere), and therefore are accelerating less, and producing less work for the same amount of energy.
So in short, you are correct in thinking that the turf applies less force, for the same amount of energy.
The equal and opposite reaction is not the energy coming back into your foot, it is the Earth moving slightly in response to the impact of your foot.
Imagine if you bolted a cannon into a massive concrete footing and fired it....apparently there is no equal and opposite reaction. But there is, the rotation of the earth would be slightly slowed for an instant, assuming the cannon is pointing East.
The Earth moves and is essentially floating in space....it is not fixed.
newton confused wrote:
Is there less force being applied into the grass compared to pavement
Yes, because in the soft surface of the grass there is initially less mass opposing it. By the time the whole ground is opposing the descending foot, it has slowed to the point where less force is needed to stop it. To decelerate it nearly instantaneously requires a much greater force, and since the ground is nearly at rest relative to the runner, that ends up meaning lots of mass. It might be different if the grass was shot upwards out of a cannon though.
and that is why there less force applied back making the athlete travel slower?
NO. That has absolutely nothing to do with the lateral motion of the runner. You slow down only if a braking force results from your footstrike. Regardless of surface, there is no reason for this to happen as long as your form is good.
If you're going to belabor the mechanics of running, start with having your foot strike the ground at relative rest horizontally. And rather than imagining yourself pushing the ground backward, start throwing yourself forward in front of the planted foot. You're not a leg, you're leg with a body on top with arms and another leg attached to it.