Double the velocity = Quadruple the energy. 

The real (more difficult) maths of this experiment involves torque inside the rolling ball, so take my flat plane model as a "guesstimate". You could probably rig a flat plane + flat block (same mass) experiment so that the forces involved are similar to this one and you'd probably get very similar results. Anyhow, here is an AI-generated article about the experiment you are doing here: Rolling ball down a pipe When a ball rolls down a pipe, several factors come into play. The ball’s motion is influenced by the pipe’s shape, the ball’s initial velocity, and the forces acting upon it. Here are some key points to consider: Force and Friction: The force of gravity pulls the ball down the pipe, while friction acts against the ball’s motion. The type of friction present depends on the surface of the pipe. If the pipe is rough, the ball will experience more friction, which can cause it to slow down or even stop. If the pipe is smooth, like frictionless ice, the ball will roll faster and maintain its velocity. Conservation of Energy: The law of conservation of energy states that the total energy of a closed system remains constant. In the case of a ball rolling down a pipe, the ball’s potential energy (stored energy due to its height) is converted into kinetic energy (energy of motion) as it rolls down the pipe. The ball’s speed and height will change as it rolls, but the total energy remains constant. Pipe Shape: The shape of the pipe affects the ball’s motion. A curved pipe can cause the ball to change direction or speed, while a straight pipe allows the ball to maintain its velocity. The ball’s speed and direction will also depend on its initial velocity and the angle of the pipe. Rolling and Sliding: When a ball rolls down a curved slope, it can experience both rolling and sliding motion. The ball’s surface can come into contact with the pipe at different points, causing it to roll, slide, or a combination of both. The ball’s speed and direction will depend on the angle of the slope and the coefficient of friction. In summary, the motion of a ball rolling down a pipe is influenced by the pipe’s shape, the ball’s initial velocity, and the forces acting upon it. The ball’s speed, direction, and height will change as it rolls down the pipe, but the total energy remains constant.

Yes Ian, there is a 'plus' sign in the equations: s1 = 9 + vt and: s2 = 36 + 2vt

Thank you for the video and demo Ian, it helps me get it down in my head, so really appreciate it mate. Hope your OK Ian, Goofy seems quiet, must be cooking up a bunch of new excuses.😂👍

Update: 1:33 1:44 I used a "floating timer" android app at these times with frame speed at 0.25, and I got 3 seconds for each, so the actual time was about 0.75 seconds which is what the μ values are suggesting for ranges closer and closer to 3ft (36"). ~~~~~~~~~~~~~~~~~~~~~~~~~~~ This might help (assumes pipe & moving object is flat, so actual value may deviate from this overestimate of net "inertial" force & acceleration down the pipe): Forces on m: In pipe (at -45° angle): Fnet~ma= mg↓+N↗+ f↖ = mg·√½ ·(1↘+1↙+1↗ +μ ↖) = mg·√½ ·(1 -μ)↘ Friction constant: μ(abs plastic on steel)≈ 0.1 to 0.3 Update: Closest I determined for Ian's experiment is more than 0.3. So, taking (mean value) μ≈0.2 , we have: a≈g·√½ ·(0.8)↘ ≈(⁹⁸/₂₅)√2↘ ≈5.54 m/s²↘ Try μ=0.1 => mult a by 0.9/0.8 => New value is a≈(9/8)(⁹⁸/₂₅)√2 => a≈ (441⁄100)√2 ≈6.24 m/s². For μ=0.3: mult a(μ=0.1) by 0.7/0.9 => New value is a≈ (7/8)(⁹⁸/₂₅)√2 => a≈ (³⁴³⁄100)√2 ≈4.85 m/s². (I worked out other values like time in pipe, pipe displacement, pipe exit velocity, range for 0.1 to 0.3 in replies below. I just recalculated everything there b/c I previous wrongly had 36" pipe displacement but that was the height!)