Download Worksheet - Uniform Circular Motion File

Le Fevre High School
SACE Stage 2 Physics
Uniform Circular Motion
1. A body travelling in a clockwise direction, moves uniformly with a
speed of 3.5 m s-1 in a circle of diameter 10 cm. (Shown opposite)
(a) Copy the diagram and mark in vectors representing the
velocity of the body at the positions A, B and C shown?
(b) Calculate its radial (ie centripetal) acceleration?
C
B
2. A body of mass 1.0 kg has a velocity of 1.0 m s-1. When it reaches a
point P, it is acted on by a force of 10 Newton which is always at
right angles to its direction of motion.
(a) Explain why it turns in a circle with a constant speed.
(b) Find the radius of the circular path
(c) Find the minimum time taken for the body to return to the point P.
10 cm
A
3. A space station has the shape of a doughnut. The distance from the centre of the hole to the
centre of the ring of "dough" is 100 m. With what speed must it be made to rotate so that a
spaceman living in the "dough" experiences the same magnitude acceleration as on the surface
of the earth?
100 m
4. A mass of 5.0 kg is whirled in a horizontal circle at one end of a string 50 cm long, the other end
being fixed. If the string when hanging vertically will just support a load of 200 kg mass
without breaking, find the maximum whirling speed in m s-1.
5. Calculate the magnitude of the force required to enable a 3.0 kg object to rotate in a circle
of 2.0 m radius at a speed of 4.0 m s-1?
2. If the engine of a car provides a forward force of 300 N, what is the total of the drag forces
acting on the car if it is moving with constant velocity?
3. A car of weight 8000 N and a truck of weight 30000 N are travelling at constant velocity on a
flat road. What is the normal force on each vehicle by the road?
4. For a car rounding a comer on a flat horizontal road,
a.
what force provides the centripetal acceleration?
b.
if the speed is doubled, what can you say about the force required to produce the
centripetal acceleration?
c.
if the radius of the curve is doubled, what can you say about the force required to
produce the centripetal acceleration?
d.
what happens if insufficient force can be supplied to achieve the required centripetal
acceleration?
Le Fevre High School
5. When rounding a corner on a street circuit, as in the figure below, why do Grand Prix racing car
drivers prefer path B to path A?
6. (a)
(b)
What provides the force for the centripetal acceleration when a road is banked at less
v2
than the angle given by the equation tan  
?
rg
If friction is not to provide any of the force for the centripetal acceleration, show that the
v2
banking angle  for a radius of curvature r and speed v is given by tan  
rg
7. Why is there a single recommended speed for a particular curve, which applies for all vehicles
irrespective of mass?
9. A curve of radius 400m is to be constructed on a freeway where the average speed is 100km/hr.
If friction is to provide no force for the centripetal acceleration, calculate the banking angle for
this speed.