CIRCULAR MOTION

(Take g = 9.8ms

^{-2})
1. Calculate the centripetal force in the following
cases:

(a) a ball of mass 150 g is spun in a horizontal circle
of radius 3m at 5 ms

^{-1}
(b) the Earth (mass 9x10

^{24 }kg) orbits the Sun once every year (3x10^{7}s), orbit radius 1.5x10^{11}m
(c) an electron (mass 9x10

^{-31}kg) orbits a nucleus in 1.6x10^{-16}s, orbit radius 10^{-10}m
2. Calculate the angular velocity of an object that
makes: (a) 25 revs per second

(b) 33.3 revs per second

(give your answers in radians per second)

3. An astronaut is trained in a centrifuge that has an
arm of length 6m. If the astronaut can withstand an acceleration of 7 g :

(a) what is the maximum number of revs per second of the
centrifuge (b) what is the maximum linear velocity of the astronaut .

4. A motorway interchange includes a smooth bend of
radius 23 m. At what angle must it be banked so that a car can take the bend in
an umpowered state at 20 ms

^{-1}?
5.
A pilot in a stunt plane loops the loop in a vertical circle of radius 0.6 km
at a constant speed of 250 km/hour. If the pilot has a mass of 75 kg calculate:

(a) the
maximum resultant force on the pilot (b) the minimum resultant force on the
pilot stating where in the loop each occurs

6. (a) Calculate the acceleration of a satellite
orbiting the Earth at a distance of 42000 km from the its centre with an orbit
time of 1 day (86400s).

(b) what might such a satellite be used for?

7. A fairground ride consists of cars suspended from
wire 5 m long. If the ride rotates so that the wires make an angle of 25° with
the vertical calculate:

(a) the orbit radius

(b) the orbit velocity

(c) the centripetal force on a car and passengers of
mass 150 kg

(d) the orbit radius for a car and passengers of mass
200 kg

8. On a roller coaster cars start from rest at the top
of a hill and then run down, going round a vertical loop of radius 6m. If the
track is frictionless calculate:

(a) the minimum velocity at the top of the loop

(b) the velocity at the bottom of the loop

(c) the height of the hill from which they must descend
assuming that the track is frictionless