Download For an object travelling with “uniform circular motion,”

SPH 4U
1.
Circular Dynamics Review
For an object travelling with “uniform circular motion,” its acceleration is
a) zero because the speed is constant
b) directed tangent to the circle
c) directed toward the centre of the circle
d) changing in magnitude depending on its position in the circle
e) directed outward from the centre of the circle
2. A fighter jet flies at 328 km/h in an arc of radius 235 m. How many “g’s” of centripetal
acceleration does the pilot experience? (1g = 9.8 m/s2)
a) 47
c) 3.8
b) 35
d) 3.6
e)
1.5
3. A rock attached to a string swings in a vertical circle. Which free body
diagram could correctly describe the force(s) on the rock when the
string is in one possible horizontal position?
4. The diagram below shows a rock on the end of a
string being whirled around in a circle in the
horizontal plane. The motion is viewed from above
and the stone is rotating clockwise. What are the
directions associated with its instantaneous
velocity and instantaneous acceleration,
respectively?
a) south, east
c) west, west
b) east, west
d) south, south
e) south, west
5. A rock is tied to the end of a 35 cm long string and whirled around in a circle that describes a
vertical plane. The tension in the string becomes zero when the speed of the rock is
a) 9.8 x 102 cm/s
c) 19 cm/s
b) 1.9 x 102 cm/s
d) 9.8 cm/s
e) 1.9 cm/s
6. A curve in the highway is banked at 15° and designed for a speed of 85 km/h. If a careful
driver rounds the curve at 70 km/h, the force of friction on the car is
a) in the same direction as the centrifugal force
b) in the same direction as the centripetal force
c) parallel to the road and towards the outside of the curve
d) parallel to the road and towards the inside of the curve
e) in the same direction as the normal force
7. Imagine you are a passenger upside-down at the top of a vertical looping roller coaster. The
centripetal force acting on you at this position
a) is perhaps the least of anywhere in the loop
b) is supplied at least partly by gravity
c) is supplied partly by the seat of the roller coaster
d) is directed vertically downward
e) all of the above
\sph4U\dynamics\478158014
8. The diagram below illustrates a car travelling with a
constant speed around a curve in the road. The curve
is banked. Which force represents the direction of
the net force acting on the car?
a) F1
d) F4
b) F2
e) F5
c) F3
9. A rock, tied to the end of a string, is whirled at a constant speed around in a horizontal circle
by a student who is holding the other end of the string. Which one of the following statements
is false?
a) The tension in the string will increase with the speed of rotation.
b) The rock will fly off along a tangent to the circle if the string breaks.
c) The circle described by the rock could be above the student’s outstretched hand if the
speed of rotation is great enough.
d) The acceleration of the rock will be directed toward the centre of the circle.
e) The tension of the string is providing the centripetal force needed to keep the rock in its
circular path.
10. A 1.0-kg and a 2.0-kg mass are each tied to the ends of identical strings and whirled around in
circles that describe a horizontal plane. The larger mass moves with a speed of 3.2 m/s. For the
tension in the two strings to be the same, the smaller mass must be moving with a speed of
a) 6.4 m/s
d) 2.3 m/s
b) 4.5 m/s
e) 1.6 m/s
c) 3.2 m/s
11. To
a)
b)
c)
d)
e)
produce an artificial gravity on board a space station
would be impossible
would require an enormous quantity of matter
is easily achieved by rotating the space station
would be possible by maintaining an inertial frame of reference
is purely science fiction
Textbook: p. 157 #12 – 19 (M/C)
12. Why does the centripetal force not appear on any free-body diagrams.
13. Why are curves in roadways often banked?
14. Describe how the acceleration of gravity on Earth’s surface would be different if both its mass
and radius were twice their present values. Provide reasons for your answer.
15. A 0.50-g insect rests on a compact disc at a distance of 4.0 cm from the centre. The disc’s rate
of rotation varies from 3.5 Hz to 8.0 Hz in order to maintain a constant data sampling rate.
a) What are the insect’s minimum and maximum centripetal accelerations during its rotation
around the disc?
b) What is the minimum value of the coefficient of static friction that would prevent the
insect from slipping off the disc at the slowest rotation rate?
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16. A ball of mass 4.0 kg is attached to the end of a 1.2 m long string and whirled around in a circle
that describes a vertical plane.
a) What is the minimum speed that the ball can be moving at and still maintain a circular path?
Provide a free-body diagram.
b) At this speed, what is the maximum tension in the string? Provide another free-body
diagram.
c) If the ball is rotated in a horizontal circle at the same speed with the end of the string
held above the head, what angle does the string make with the horizontal?
17. A rock of mass 4.0 x 102 g is tied to one end of a string that is 2.0 m in length. Holding the
other end above his head, a boy swings the rock around in a circle whose plane is parallel to the
ground.
a) If the string can withstand a maximum tension of 4.5 N before breaking, what angle to the
vertical does the string reach just before breaking?
b) At what speed is the rock travelling just as the string breaks?
18. A pilot of mass 60.0 kg is flying her plane in a vertically oriented circular loop. Just at the
bottom of the loop, the plane’s speed is 1.8 x 102 km/h and the pilot feels exactly four times as
heavy as she normally does.
a) What is the radius of the loop?
b) At what speed must she be flying at the top of the loop in order to feel weightless?
19. Mackenzie High School is installing a midway ride to help pay for the damage done by the
previous grad trip. The physics class is responsible for one such ride where the customers
rotate in a vertical circle (horizontal axis) with their back against a cylindrical wall. When the
ride gets up to sufficient speed, the riders feel weightless at the top of the circle. If the
radius of the ride is 3.00 m, what is
a) the period of the ride?
(3.48 s)
b) the normal force on a 70 kg rider at the bottom of the circle?
(1.37 x 103 N)
c) the speed of the thrill seekers?
(5.42 m/s)
20. On one snowy December day, the coefficient of friction on a 21° banked curve is only 0.2. If
the radius of the curve is 100 m, what range of speeds is possible?
(12.9 m/s to 24.9 m/s)
21. For uniform circular motion, what value is the constant of proportionality? Its value can be
determined experimentally as long as certain relationships exist. Explain or describe them.
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