1) Gravitational potential energy
In fact, gravitational potential energy is given by: \(GPE=mgh\)
where m is the mass of the roller coaster, g is the gravitational acceleration and h is the heigth. Therefore, when the roller coaster goes uphill, the height h increases and the roller coaster gains gravitational potential energy.
2) The relationship between potential and kinetic energy is:
\(M.E.=K.E.+G.P.E.\)
where ME is the total mechanical energy, KE is the kinetic energy, GPE is the gravitational potential energy. Since the value of ME is constant (when no friction is present), this means that when KE increases, GPE decreases, and vice-versa.
3) If friction is removed from the track, the roller coaster would move forever. In fact, in the equation written in part 2), ME is constant only in case there is no friction - when friction is present, part of the energy is lost due to the friction, so the total ME available decreases little by little until it becomes zero, and the roller coaster cannot move anymore.
4) It matters because it affects the magnitude of the friction. In fact, friction is given by
\(F=\mu mg\)
where \(\mu\) is the coefficient of friction, m is the mass ,and g the gravitational acceleration. When the number of carts is increased, the mass increases, therefore the friction increases as well.
