Relationship between initial speed of cart and distance repelled by magnets.

[ongfufu]

1. Determining the relationship between initial speed of a cart (with magnets, aligned with and moving towards magnets on a wall) and the stopping distance from the wall)



2. Kinetic energy(Ke)=Magnetic potential energy(Mpe)
Ke=mv^2/2
Mpe=km1m2/r
mv^2/2=km1m2/r
v is proportional to (r^1/2)
K$$_{e}$$=$$\frac{mv^{2}}{2}$$
M$$_{pe}$$=k$$\frac{m_{1}m_{2}}{r}$$
$$\frac{mv^{2}}{2}$$=k$$\frac{m_{1}m_{2}}{r}$$
v is proportional to $$\frac{1}{\sqrt{r}}$$

3. I think speed is proportional to inverse square root of the stopping distance.

So a cart with magnets taped to the front end is pushed through a photogate, which measures speed of the cart, towards the wall with magnets aligned with those on the cart. The cart starts 20cm away from the wall. By varying the speed of the cart, I measured how far the cart was repelled by the magnets on the wall.

 

[jbsteele]

I found that the speed of the cart and the stopping distance from the wall were inversely proportional to each other, with the stopping distance decreasing as the speed increased. This means that the faster the cart was moving, the shorter the stopping distance from the wall.

 

[thomate1]

Based on the equations provided, it can be seen that the speed of the cart is directly proportional to the inverse square root of the stopping distance from the wall. This means that as the initial speed of the cart increases, the stopping distance from the wall decreases. This relationship can also be observed in real-world scenarios, as objects with higher initial speeds tend to cover shorter distances before coming to a complete stop.

Furthermore, the equations also show that the kinetic energy of the cart is equal to the magnetic potential energy between the magnets on the cart and the wall. This means that the initial speed of the cart is directly related to the strength of the magnetic field and the distance between the magnets. As the initial speed of the cart increases, so does its kinetic energy, resulting in a stronger repulsion force between the magnets and a shorter stopping distance from the wall.

In conclusion, the relationship between the initial speed of the cart and the stopping distance from the wall can be described by the inverse square root function. This relationship is influenced by the kinetic energy and magnetic potential energy of the system, and can be further explored and understood through experimentation and analysis.