To keep the forces on the riders within allowable limits, many loop-the-loop roller coaster rides are designed so that the loop is not a perfect circle but instead has a larger radius of curvature at the bottom than at the top. Explain.

Solution 24DQ Step 1 of 3: There is a centripetal force that is pushing the trucks of the coaster towards the center the loop. Newton's first Law of Motion of motion tells us that, without this force, the coaster would like to travel in a straight line and at constant speed. The centripetal force is pushing the coaster around in a circle.When accelerating around in a circular path, the magnitude of the acceleration is proportional to the ratio of the speed squared over the radius of the curve. The tighter the radius, or the higher the speed, the greater the acceleration. The slowest speed that an coaster can go around a loop upside down is at the limit at which the centripetal force is provided entirely by gravity. Roller coasters are typically not powered vehicles; at the start of the ride they are charged with gravitational potential energy then transfer this backwards and forwards to kinetic energy as they ride up and down the track. If the loop were a perfectly circular arc then the trucks of the coaster would need to start at the bottom of the loop with sufficient enough kinetic energy such, after converting much of this to potential energy to climb, still has sufficient energy to just make it over the top. Step 2 of 3: If the coaster starts are rest at the top of the ride, the velocity of the coaster at any point can be determined using the principle of Conservation of energy. (In the absence of resistances such as friction and air)