Designing a roler coaster is very tricky. Patrons of theme and amusement parks want to be thrilled , but generally do not want to be injured.
Downard accelerations of greater than 10 g cause bodily harm.
Negative (i.e upward) accelerations of greater than about 5 g also cause damage ( "red out")

The drawing shows a car a the left which is going to the right where therre is a loop , the maximum hight of the loop (or the diameter of the loop represente by a circle is "h").

1) After a thriller first drop, a roller coaster car travels at speed Va into a loop of height h=15m. Find the range of velocities such that the net acceleration at the top of the loop is less than 5g and more than 0g.
Assume the car travels with speed Va all the way through the loop.

2) Compute the total work done by the car to reach the top of the loop.

Solution Preview

Speed Va m/sec
radius = r = 15/2 = 7.5 m
Ac = Centripetal Acceleration = Va^2/r (m/s^2)
1g = 9.8 m/s^2
Ac = Va^2/(7.5*9.8) g's = Va^2/0.0136 g's
At the top of the coaster, since the weight acts vertically down, the net ...

Solution Summary

The solution provides step by step calculations for the speed of a car going along the roller coaster track.

A 350 rollercoaster starts from rest at point A and slides down the frictionless loop, which is shown in the accompanying figure (see attachment)
How fast is this rollercoaster moving at point B? v = ? m/s
How hard does it press against the track at point B? F = ? N

A rollercoaster has an initial speed of 9.50 m/s at the top of the first hill, which is 44.00 m above the ground. Neglecting friction, what will be the speed of the rollercoaster at the top of the next hill, which is 26.00 m above the ground?

The maximum velocity of a rollercoaster depends on the vertical drop from the top of the highest hill to the bottom of that hill. The formula: (see attached), gives the relationship between maximum velocity, V(h) in feet per second, and height, h in feet.
1. Identity the independent variable, dependent variable.(Must use the

A rollercoaster car starts from rest and rolls down a frictionless track, reaching speed v_f at the bottom.
a. If you want the car to go two times as fast at the bottom, by what factor must you increase the height of the track?
b. Does the answer to part (a) depend on whether the track is straight or not? Explain.

Suppose the rollercoaster in Fig. 8-29 (attached) (h1 = 32 m, h2 = 13 m, h3 = 20) passes point A with a speed of 3.00 m/s. If the average force of friction is equal to one fifth of its weight, with what speed will it reach point B? The distance traveled is 55.0 m.

The 65 kg man in the rollercoaster car is sitting on a bathroom scale. If he is traveling at 40.4 m/s at the point shown and the radius of the vertical coaster track is 62 meters to the nearest newton, what does the scale read?
What would be the answer if the rollercoaster was at the bottom of the track?
(See attached fi

A rollercoaster 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 2.3 times her weight as she goes through the dip. If r = 29.0 m, how fast is the rollercoaster traveling at the bottom of the dip?

At what minimum speed must a rollercoaster be traveling when upside down at the top of a circle if the passengers are not to fall out? Assume a radius of curvature of 9.27 m.

A rollercoaster car of mass 320 kilograms(including passengers) travels around a horizontal curve of radius 35 meters. Its speed is 16 meters per second. What is the magnitude and direction of the total force exerted on the car by the track?