Exemplar for internal assessment resource Physics for Achievement Standard 91522
The Physics of a Vertical Loop on a Rollercoaster
As the carts approach a loop it must have all of the kinetic energy (and so velocity) required
to complete the loop because of the aforementioned law (the conservation of energy) this is
the challenge engineers are faced with in designing a loop in a rollercoaster. Loops in
rollercoaster's can give the feeling to passengers that they are weight less or heavier than
they normally are. To understand why this happens we need to understand the force that
holds the carts to the tracks. We can recognize that there is a force holding the carts to the
tracks because the carts both have a continually changing velocity, because of the
conservation between kinetic and gravitational potential energy, and because they have a
continually changing direction of travel. This results in an acceleration and force towards the
centre of the circle which is called a centripetal force and should not be confused with the
fictional centrifugal force (the diagram opposite illustrates the centripetal acceleration).
There is one more force that acts on the carts and that is the weight of the carts, this always
acts towards the centre of the earth. The passengers have one a more force acting on them
and this is the support force which is how people feel the effects of gravity. This is because
you don't feel gravity pushing you into the cart but you feel the cart pushing on you with an
equal and opposite force, Newton's 3rd law,
(the diagram above). When the carts are at the bottom of the loop the passengers feel
heavier than normal because the support force is exerting a greater force on the passengers.
As the support force and the centripetal force/acceleration are acting in the same direction
then this results in an increased net force acting on the passenger towards the centre of the
circle which feels like the support force. Therefore as the support force increases what the
passengers feel as their weight also increases.
There is one more element of a rollercoaster loop that has yet to be explained and that is
what happens at the top of the loop. The diagram to the right illustrates the centripetal
acceleration direction.
© NZQA 2015
Exemplar for internal assessment resource Physics for Achievement Standard 91522
At the minimum speed for the carts to go around the loop the passengers would feel
weightless at the top. This is because the minimum centripetal acceleration required to go
around the loop is the same as the acceleration Elute' = 0 due to gravity that acts on the
mass of the passenger. As illustrated in the diagram
(imagine the seat is upside-down) the centripetal force which is the force that changes the
passenger's direction constantly is the weight force (the acceleration of a person’s mass due
to gravity). This means that there is no support force required by the cart to keep the person
in the seat. However this would be extremely dangerous to put into practice in real life as it
would take only one error for people to die so few rollercoaster's have this feature in their
loops. What is more common is for people to feel slightly lighter because when the carts are
at the maximum position they have a greater velocity than required and this results in a
support force but one that is smaller than normal.
© NZQA 2015