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A Suitably Sturdy Slide

Falling rapidly towards the ground is usually bad news. But put a slide beneath you, and you're guided to a safe landing. Pools and water parks take this to an extreme, with long, elaborate slides that descend several stories.

How do engineers decide how strong these slides need to be? The slide, and the structure supporting it, must always push against you with enough force to propel you through its twists and turns. If not, the slide collapses, which would take the fun out of the whole ordeal.

As you glide down a slide, it exerts a force on you. We call this force the reaction force. It appears whenever you push against something solid.

The reaction force is an example of Newton's third law of motion:

Whenever one object applies a force on another, the second object applies a force on the first object with the same magnitude but in the opposite direction.

Standing on a flat surface is a simple illustration of this law. The weight of your body pushes down on the surface, and the surface pushes back with a reaction force against your feet. In this example, you're not accelerating, so your weight and the reaction force are equal, making the net force on you zero.

On the slide, Newton's third law works almost the same way. Your body pushes on the slide as you move, and the slide reacts by pushing back. The difference is when you're sliding, your body is accelerating, so the reaction force isn't equal to your weight.

So how big is the reaction force when you're accelerating? The short answer is it depends on how big your acceleration is. A more detailed answer depends on the details of your motion.

At any instant after you start sliding, your velocity v\mathbf{v} tells you where you will be a very short time later. Velocity says how fast you're going and in what direction.

Your velocity changes as you start down the slide. This change is due to your acceleration, which describes how quickly your velocity is changing. The more quickly your velocity changes over time, the greater your acceleration.

Assuming you stay on the slide, your velocity can only ever point along the surface of the slide right underneath you. If the slide curves, your velocity hugs the curve, and this requires a certain acceleration. You can see how the velocity and acceleration change over time in this animation:

Sometimes people refer to a reaction force as a force of constraint. When your motion is constrained to a surface, as on the slide, the reaction force is always equal to the required force to keep you moving continuously along the surface.

Other than being dependent on your motion, the reaction force behaves like any other force. It combines with other forces on you, such as weight and friction, to produce your net force. Also, if at any point the reaction force becomes zero, you lose contact with the slide's surface.

Today's Challenge

The acceleration of a person on a slide is the combined effect of their weight, which always points directly downwards, and the reaction force, which points directly away from the surface of the slide.

At which point in this diagram will the reaction force be the greatest?

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