Physics of Fitness Fridays - Jump! For My Love (Pt 2)
Last time I talked about what happens when you take off from a jump and how high you can go. Today I’ll focus on what happens as you push yourself up off of the ground. (I’m skipping the part when you “preload” to keep things simple.)
When you are crouching at the bottom of the jump, there are two forces acting on you. There’s the force of gravity, or your weight W; this is equal to your mass times the acceleration of gravity, which is constant. Then there is the Ground Reaction Force, or Fgr. This is the force of the floor pushing back on you, and translates to the amount of force you push on the floor. (In physics, we talk about external forces, not internal ones!). The total force acting on you when you jump is Ftotal = Fgr – W (Weight is subtracted here because it points downward).
Force and acceleration are connected; acceleration is just the total force acting on an object divided by its mass. If a force is > 0, then so is the acceleration and the object speeds up. And if the force is < 0, so is acceleration and the object slows down.
Let’s return to the bottom of the jump. Before you start, you are stationary, thus Ftotal = 0 and the two forces cancel, giving Fgr = mg. Suppose you were standing on a scale as you prepared for a jump. That means that at this point, the scale would read your “normal” weight.
As you start the jump, your body pushes against the ground, and the ground pushes back! The reaction force accelerates your body from rest, therefore, Ftotal > 0 and Fgr > W. So now your scale would read a lot more than your normal weight!
At a certain point in the motion, you reach your maximum upward speed. Surprise--it doesn’t happen as you take off in the air! You would know when you reached max speed because you are no longer accelerating, and the scale would return to your normal weight.
During the final stage before takeoff, you are actually slowing down. Your weight will be less than normal, and decrease until it drops to zero—this is when your feet lose contact with the scale and you are airborne!
So the greater the force, the greater the speed, but your speed at liftoff is always less than what you achieve while in contact with the ground. Who knew what you’d learn when you look at what happens before you leap?
For the record…I actually tried to “measure” my weight during a jump. It didn’t work out so well, as you can see in the video below. Suffice to say, my scale isn’t sophisticated enough to capture what’s going on. Did you know that they actually make force platforms that will measure the force exerted by each foot when you jump? Pretty cool! I’d love one for the home, but they’re a little out of my price range!
Poorly attempted science measurement. The video is upside down, but if you look closely you can sorta see my weight go up and down from 145ish.
By the way, here are some interesting references that talk about jumping and force plates The first one is where I got a lot of this blog post.