Transcript Physics_A2_Unit4_08_FairGrounds

Book Reference : Pages 28-29
1.
To apply what we have learnt about circular
motion to rides at the fairground
2.
To consider three particular cases of motion:
•
The big dipper
•
The long swing
•
The “centrifuge” wall of death
At the bottom of a big dipper you are pushed
into your seat and feel “heavier”...
Centre of curvature
velocity
mg
At the bottom of the dip at speed v with radius r,
Resolving the vertical forces:
S – mg = mv2 / r
S = mg + mv2 / r
The “extra” weight you experience when feeling
“heavy” is given by the centripetal force
Consider a person of mass m on a very long
swing of length r
To winch
r
Fixed point
Initial position
S
Velocity
mg
As the swing is released we can consider the
conservation of energy, loss in potential energy is
the gain in the kinetic energy
mgh = ½mv2
 v2 = 2gh
The passenger is on a circular path with radius r.
At the bottom of the swing the support force S
acts against the person’s weight mg. This
provides the centripetal force:
S – mg = mv2/r
Substituting for v2:
S – mg = mv2/r
S – mg = 2mgh/r
S = mg + 2mgh/r
The person “feels heavier” by 2mgh/r, if the
swing drops through 90°, then the extra support
force is twice the persons weight (mg)
Consider a fairground ride which spins fast
enough to keep you in place even when upside
down at the top of the ride....
Velocity
Reaction R &
weight mg
Rotation
The wheel turns fast enough to keep the
passenger in position as they pass over the top.
At the top, the reaction R acts downwards and
together with the weight provides the
centripetal force:
mg + R = mv2/ r
R = mv2/ r – mg
At a certain speed v0 such that v02 = gr, then the
reaction from the wall will be zero
A car on a big dipper starts from rest and descends
though 45m into a dip which has a radius of
curvature of 78m. Assuming that air resistance &
friction are negligible. Calculate:
a. The speed of the car at the bottom of the dip
b. The centripetal acceleration at the bottom of
the dip
c. The extra force on a person with a weight of
600N in the train
A swing at a fair has a length of 32m. A passenger of
mass 69kg falls from the position where the swing is
horizontal. Calculate:
a. The speed of the person at the lowest point
b. The centripetal acceleration at the lowest
point
c. The support force on the person at the lowest
point
A wall of death ride at the fairground has a radius of
12m and rotates once every 6s. Calculate:
a. The speed of rotation at the perimeter of the
wheel
b. The centripetal acceleration of a person on
the perimeter
c. The support force on a person of mass 72kg at
the highest point