(Solved): Harry Potter Broomstick Ride has just been opened at Wally-World in Orlando. A two-person cart is p ...

Harry Potter Broomstick Ride has just been opened at Wally-World in Orlando. A two-person cart is pushed back 3 meters into a large spring and then released from rest. The cart follows a track up over a hill that is $25\mathrm{m}$ tall, around a loop-de-loop, and then comes to a stop on a level section of track. The track is "magically frictionless" for most of the ride, from the release point at $\mathbf{A}$ to point $\mathbf{C}$. After point $\mathbf{C}$, the track is rough such that the coefficient of kinetic friction is ${\mathrm{u}}_k=1.2$. The mass of the cart with two riders is $300\mathrm{kg}$. The speed of the cart with two riders is found to be at point $\mathbf{B}$. (a) Find the spring constant for the spring. $\mathrm{N}/\mathrm{m}(\pm 100\mathrm{N}/\mathrm{m})$ (b) What is the magnitude of the normal force exerted by the track on the $300?\mathrm{kg}$ cart (including riders) at point $\mathbf{B}$ ? $N(\pm 10N)$ (c) If the friction requires a distance of $20\mathrm{m}$ to stop the cart (with two riders) at point $\mathbf{D}$, what is the height $\mathbf{H}$ of the final level portion of track?