We can break that diagonal motion down into horizontal and vertical parts; for now, let’s focus on just the former. Let’s say you start with a horizontal velocity (in1) of –1 meter per second and bounces with a horizontal speed (in2) of +1 m/s. The change in sign indicates the reversal of direction. Think of it as moving back and forth along the x-axis of a coordinate plane, negative on the left, positive on the right.
Please note that your speed remains the same, but the speed changes. (Remember, speed has a direction.) In fact, because Your horizontal speed is reversed and you gain a huge boost in speed. (v2 – v1) = (1 – (–1)) = 2This gives you greater impact acceleration, greater normal force, and more friction. Bouncing back and forth is the key to overcoming gravity in this stunt.
So how much force would you have to exert to perform one of these bounce jumps against the wall? Let’s say you have a mass of 75 kilograms and a coefficient of friction of 0.6, which is probably conservative for rubber soles.
To begin with, the friction force (FF) must be equal to or greater than the gravitational force (mg). The intensity of the gravitational field on Earth (gram) is 9.8 newtons per kilogram. Therefore, the gravitational force, (Mxg) = 75 x 9.8 = 735 newtons.
Now remember, the friction force is the normal force multiplied by the coefficient of friction (FF = μN). Therefore, to achieve a minimum friction force of 735 newtons, we need a normal force of at least 1225 newtons (FF/μ = 735/0.6 = 1,225).
Both forces, gravity and the normal force, are pushing on you, so we need to add them together to get the net force. Since they are perpendicular, we can easily calculate the vector sum as 1429 newtons. (Take note, kids: Wanna be parkour heroes? Take linear algebra.)
That means you have to push back with the same force (because forces are an interaction between two things). 1429 newtons is a force of 321 pounds. That’s significant but not impossible. Do it eight times in quick successionBut? It’s not that easy.
How much time do you have to turn around? With the normal force and the mass of the person, we can calculate the horizontal acceleration tounknown. By definition, that in turn is equivalent to the change in velocity per unit of time (Δt), so we can use this to solve for the time interval:
If we plug in our numbers, we get a time interval of 0.12 seconds. In other words, if you hesitate, you fall. In short, if you want to do this incredible parkour stunt, you need to be strong, fast, and brave, because if you run out of newtons halfway up, the descent is much faster than the ascent.
