Demonstration of Newton's First and Second Law

To be fair I couldn't explain Newtonian Mechanics to kids because I'd want to jump straight into the maths. There were a couple of demos which did cover the topics as long as you remembered that they were a simplified view.

 

Things like this I'd want to use energy equations and ignore loss (A-Level mechanics). If loss is important you start getting complex. Ignoring loss, the kinetic energy of the ball at any point is equal to the change of potential energy due to loss of height. This technique also works for the toy elephant launcher and is easier than integrating Newton's second law.

 

½mv² = mg(H-h) - where (H-h) is height lost , g the acceleration due to gravity, and m, the mass of the ball, cancels

 

The explanation did give the forces on the balls as "Gravity" and "Friction". I've drawn gravity as "mg", but my other force is "Reaction" which is perpendicular to the ramp. The resultant force is the accelerating force on the ball. My arrows were not drawn to scale so may or may not line up.

 

Friction is significant because it will cause the balls to rotate. Energy equations would still work, only now we must include the rotational energy of the ball. Interestingly the mass cancels out again, as does the radius:

 

Moment of Inertia for sphere around centre = I = 2/5 mr²

Rotational Energy = ½Iω²

Rotation ω = speed along ramp / radius = v/r

Rotation Energy = 1/5 m r² v² / r² = 1/5 mv²

 

So the speed of the ball at any point, ignoring loss and assuming no slippage, comes out as

 

speed = √(10/7 g (H-h))

 

Which means that it doesn't matter what size ball you roll down the ramp as long as it doesn't fall through the gap or hit the other part of the loop or is so large and light or rough that loss becomes significant.

 

For the kids though - a chance to roll some balls down a ramp and hear a loud clang as they hit a metal plate hidden in a suitcase on stage.

Done