

12) (5 points) A roller coaster car moves around a vertical circle. At the bottom of...
You are testing a new roller coaster ride in which a car of mass m moves around a vertical circle of radius R. In one test, the car starts at the bottom of the circle (point A) with initial kinetic energy Ki. When the car reaches the top of the circle (point B), its kinetic energy is Ki/4, and its gravitational potential energy has increased by Ki/2. What was the speed of the car at point A, in terms of...
A roller coaster car travels around a vertical loop. At the top of the loop, where it is upside down, it is moving at a speed of 10 m/s. Given that the loop has a radius of 8.0 m, a) What is the value of the car’s centripetal acceleration at that instant in time? b) A 55 kg passenger is in the car. Draw a free‐body diagram showing all the forces acting on the passenger. c) What is the magnitude...
A roller-coaster car shown in the figure on the right is released from rest from a height h and then moves freely with negligible friction. The roller-coaster track includes a circular loop of radius R in a vertical plane. a. First suppose the car barely makes it around the loop; at the top of the loop, the riders are upside down and feel weightless. Find the required height h of the release point above the bottom of the loop in...
A car in an amusement park roller coaster ride rolls without friction at the top of a hill. The car begins at a height h from the top of a hill. A the bottom, the car then goes through a vertical loop where the car is upside down at the loop\'s top. If the radius of the loop is 20.0m, what is the minimum height h such that the car moves around the loop without falling off the track at...
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r = 20.0 m, how fast is the roller coaster traveling at the bottom of the dip?
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to three times her weight as she goes through the dip. If r = 18.0 m, how fast is the roller coaster traveling at the bottom of the dip? The answer is NOT 26.56
3. A frictionless roller-coaster goes around a circular loop of radius 11 m. It enters the bottom of the loop going 32 m/s. Find the speed of the roller-coaster when it gets to the top of the loop 4. For the loop in the previous problem find the velocity of the roller-coaster as a function of height off the ground. Use that to find the centripetal acceleration as a function of height. Plot the centripetal acceleration as a function of...
One portion of the track of a toy roller coaster is bent into a full vertical circle of radius R. A small cart rolling on the track enters the bottom of the circle with a speed √gR. Show that this cart will fall off the track before it reaches the top of the circle, and find the (angular) position at which the cart loses contact with the track.
1. A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r = 28.7 m, how fast is the roller coaster traveling at the bottom of the dip? 2. A 0.21-kg ball on a stick is whirled on a vertical circle at a...
Problem 1 You are designing a roller coaster, shown in the figure below. An empty car has a mass of 120 kg. The radius of the vertical loop in the track is 12.0 m and the bottom of the loop is 5.0 m above the ground. Assuming the roller coaster is frictionless, how high must the car initially climb above the ground (point A) such that the speed of the car is 25.0 m/s at the top of the loop...