Question

The Sidewinder is a shuttle type steel rollercoaster. The rollercoaster cart starts at the bottom of the frictionless track and is accelerated from a stand still over a distance of 7 meters. Then the cart enters the loop, rises to the top with just enough velocity to keep from stalling at the top of the loop. Gaining velocity the cart finishes the loop, bottoms out, and then rises up the vertical segment of the track. After stalling out at a maximum height the cart then return its path back to the starting point. This is a frictionless track with the radius of the loop measuring 7 meters. The mass of the cart filled with riders weighs 4000 kg.

a. Determine the minimum speed the cart must have at the top of its arc so that the cart continues moving in a circle.

b. Calculate initial velocity (Vo) that must be obtained to have the velocity needed at the top of the loop.

c. What is the acceleration of the cart that must be obtained in “g’s”?

d. What is the Kinetic Energy of the cart as it enters the loop? Top of the loop?

e. What is the Kinetic Energy as it exits the loop?

f. How high up the vertical climb does the cart climb?

RIDE #2: Gravitron In this ride passengers stand inside an 18.0 m diameter rotating ring. After the ring has acquired sufficient speed, the floor drops out from under the passengers! Much to the surprise of the passengers they do not fall. The Gravitron rotates at 25 rpm and a rider’s mass has an average of 58 kg.

a) What is the coefficient of friction between the person and the wall that allows the rider to stick to the wall?

b) What is the acceleration the rider feels in “g’s”?

c) If the Gravitron catastrophically fails and comes to an immediate stop when it is at maximum speed what is the kinetic energy of the rider at that moment.

Ride #3 - Pirate Swing One of my son’s favorite rides is the pendulum pirate swing. It is a pirate ship that swings like a pendulum (back and forth) from a center pivot point 50 ft above the ship. The ship can is 12 feet long with a mass of 1000 kg and can swing through a maximum angle of 40 degrees.

a) What is the maximum velocity that the pirate swing reaches?

b) What is the maximum potential energy of the swing an where does it happen?

c) What is the maximum kinetic energy of the swing and where does it happen?

Answer 1

F=ma T+mg = T-0->minimum speed my v=-/gr = /9.8 x7 =8.28 m/s 8.28 at 8.28 ngS. 8.28 t_0.845 9.8