Download Circular motion: Extra problems

Circular motion: Extra problems
For all these problems, pay attention to units when you are calculating anything!
You will have to look up conversion factors when necessary!
*** most challenging problems
1. Is the following statement correct? “ The race car rounds the turn at a constant
velocity of 90 miles per hour.”
2. Describe the path of a moving object when the acceleration is
a. Perpendicular to its velocity
b. Parallel to its velocity
3. A bicycle wheel rotates at a constant 25 rev/min. Is its angular velocity
increasing, decreasing or remaining constant?
4. What does the spin cycle of a washing machine do to the clothes and water?
Explain in terms of forces and Newton’s laws.
5. The outer edge of a truck tire has a radius of 45 cm and a linear velocity of 23
m/s.
a. What is the angular velocity in rad/s, in rev/sec?
b. What is the period?
6. A propeller spins at 1880 rev/min.
a. What is its angular velocity in rev/sec, in rad/sec?
b. What is the period?
c. If the propeller’s radius is 0.5 m, what is the linear speed at the tip of one
of the propellers?
7. You are in car making a sharp turn at high speed. Why do you feel as if you are
being thrown to the outside of the turn?
8. You are at Six Flags taking data on the teacups ride. A teacup makes 40
revolutions in 13 seconds. What is the frequency and period?
9.
How are velocity, friction and radius related to a car’s ability to turn in a
circular path?
10. How does banking of a racetrack affect a car’s ability to turn?
11. A 55.0-kg ice-skater is moving at 4.00 m/s when she grabs the loose end of
a rope, the opposite end of which is tied to a pole. She then moves in a
circle of radius 0.800 m around the pole. (a) Determine the force exerted
by the horizontal rope on her arms. (b) Compare this force with her
weight.
12. ***A sample of blood is placed in a centrifuge of radius 15.0 cm. The mass
of a red blood cell is 3.0 × 10–16 kg, and the magnitude of the force acting
on it as it settles out of the plasma is 4.0 × 10–11 N. At how many
revolutions per second should the centrifuge be operated?
13. The cornering performance of an automobile is evaluated on a skid pad,
where the maximum speed that a car can maintain around a circular path
on a dry, flat surface is measured. Then the centripetal acceleration, also
called the lateral acceleration, is calculated as a multiple of the free-fall
acceleration g. The main factors affecting the performance of the car are its
tire characteristics and suspension system. A Dodge Viper GTS can
negotiate a skid pad of radius 61.0 m at 86.5 km/h. Calculate its maximum
lateral acceleration.
14. A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m,
rotating with an angular speed of 3.00 rad/s. (a) What is the child’s
centripetal acceleration? (b) What is the minimum force between her feet
and the floor of the carousel that is required to keep her in the circular
path?
15. ***A 40.0-kg child takes a ride on a Ferris wheel that rotates four times
each minute and has a diameter of 18.0 m. (a) What is the centripetal
acceleration of the child? (b) What force (magnitude and direction) does
the seat exert on the child at the lowest point of the ride? (c) What force
does the seat exert on the child at the highest point of the ride? (d) What
force does the seat exert on the child when the child is halfway between
the top and bottom?
16. Use a real world example to explain the relationships between
a. linear speed
b. radius,
c. period
d. angular speed
e. centripetal acceleration
f. centripetal force
g. mass
You can make up numbers to help explain. Make sure your
numbers are realistic.
17. *** It has been suggested that rotating cylinders about 10 mi long and 5.0
mi in diameter be placed in space and used as colonies. What angular
speed must such a cylinder have so that the centripetal acceleration at its
surface equals the free-fall acceleration on Earth, i.e. ~ 10 m/s2 ?
18. A 2.10 m rope attaches a tire to an overhanging tree limb. A girl swinging
on the tire has a linear speed of 2.50 m/s. If the magnitude of the
centripetal force is 88.0 N, what is the girls mass?
19. A bicyclist is riding at a linear speed of 13.2 m/s around a circular track.
The magnitude of the centripetal force is 377 N, and the combined mass of
the bike and the rider is 86.5 kg. What is the track’s radius?
20. A 905 kg car travels around a circular track with a circumference of 3.25
km. If the magnitude of the centripetal force is 2140 N, what is the car’s
linear speed?
21. A kid swings a yo-yo parallel to the ground and above his head, the yoyo has a centripetal acceleration of 250 m/s2. If the yo-yo’s string is 0.50 m
long, what is the yoyo’s linear speed?