Tutorial 7 : Motion in a circle
6. The diagram represents
a cyclist making a left
turn on a rough road
surface at a constant
speed v as viewed from
behind. The total mass
of the bicycle and rider is
m and their combined
centre of gravity is at G.
If R is the resultant force on the normal
reaction and frictional force, which
vector diagram represents the directions
of the forces acting on the bicycle and
its rider?
R
R
G
G
mv
r
2
m
g
A
m
g
B
R
R
G
mv 2
r
m
g
C
mv 2
r
G
m
g
D
mv 2
r
7. [J85/II/8 (part)]
An aircraft is traveling at a constant
speed of 180 m s-1 in a horizontal circle
of radius 20 km. A plumbline, attached
to the roof of the cabin, settles at an
angle θ to the true vertical while the
aircraft is turning.
(a) Find the centripetal acceleration of
the aircraft.
(b) Name the forces which act on the
bob of the plumbline and draw a
labeled diagram to show the
directions of these forces and of
their resultant (Indicate the centre of
circle on your sketch)
(c) Find the angle θ.
(d) Shows by means of a simple sketch
of the cross-section of the aircraft
and its cabin how the plumbline is
oriented with respect to the aircraft.
o
[1.62 m s-2 ; 9.4 ]
8. [N06/P3/3(part)]
(a) A theme park ride is illustrated in the
figure below. The carriages accelerate
down the slope and then loop the loop
on a circular section of the track. The
radius of the circular section of track is
8.6 m.
(i) Find the minimum speed of the
carriages at the top of the circular
track so that the carriages remain in
contact with the track.
(ii) In practice, it is essential for
designers to build in a considerable
safety margin. Each carriage and its
passengers has a total mass 800 kg.
At the top of the loop, the carriage
travels at
17 m s-1. Calculate the
force that the track exerts on the
carriage at the top of the loop.
(b) For the carriage in (a) to have a speed of
17 m s-1 at the top of the loop, it must
have fallen from a height of at least x.
(i) Deduce a value for x.
(ii) State an assumption that you made
in making this deduction.
[9.2 m s-1 ; 19kN ; 32 m]