Download 1 - Manhasset Public Schools

Name:
AP Quiz: Circles
C
1-4. A 4-kilogram mass is traveling in a uniform
circular motion on a 1-meter cord. The tension in the cord is 8 N.
1.
[a]
[b]
[c]
[d]
What is the magnitude of the ball’s acceleration?
1 m/s2
2 m/s2
8 m/s2
4 m/s2
B
2. The direction of the net force acting on the object
at position is A
[a]
[b]
[c]
[d]
A
3. If the object’s speed is doubled and the radius is unchanged, the force acting on it will
be
[a] doubled
[b] halved
[c] quadrupled
[d] quartered
4. If the mass of the object was doubled while the speed and the radius remain
unchanged, the acceleration of the object will
[a] double
[b] half
[c] quadruple
[d] not change
5. A car rounds a horizontal curve of
constant radius at a constant speed. Which
diagram best represents the directions of
both the car’s velocity, v, and acceleration,
a?
1.
3.
2.
4.
6. A student on an amusement park ride moves in a circular path with a radius of 3.5
meters once every 8.9 seconds. The student moves at an average speed of
[a] 0.39 m/s
[b] 1.2 m/s
[c] 2.5 m/s
[d] 4.3 m/s
7. A ball attached to a string is moved at constant speed in a horizontal circular path. A
target is located near the path of the ball as
shown in the diagram.
At which point along the ball’s path should the
string be released, if the ball is to hit the
target?
1.
2.
3.
4.
A
B
C
D
8. A ball of mass M at the end of a string is swung in a horizontal circular path of radius R at
constant speed V. Which combination of changes would require the greatest increase in the
centripetal force acting on the ball?
(1) doubling V and doubling R
(2) doubling V and halving R
(3) halving V and doubling R
(4) halving V and halving R
Questions 9-10 refer to the diagram at the right. A
1200-kilogram car traveling at a constant speed of
9.0 meters per second turns at an intersection. The
car follows a horizontal circular path with a radius
of 25 meters to point P.
9. The magnitude of the centripetal force acting on
the car as it travels around the circular path is
approximately
(1) 3.9 x 103 N
(2) 1.2 x 104N
(3) 4.3 x 102 N
(4) 1.1 x 104N
10. At point P, the car hits an area of ice and loses
all frictional force on its tires. Which path does the
car follow on the ice?
(1) A
(2) B
(3) C
(4) D
11. A 1.5 kg block is attached to a 2.0 kg block on a table as shown. When released
block A accelerates to the right at 2.0 m/s2.
a. On the diagram below, draw a Freebody diagram of the forces acting on block B.
B
b. Find tension in the string. [2]
c. Find the coefficient of kinetic friction acting between block A and the table. [3]
12. A coin C of mass 0.0050 kg is placed on a horizontal disk at a
distance of 0.14 m from the center, as shown above. The disk
rotates at a constant rate in a counterclockwise direction as seen
from above. The coin does not slip, and the time it takes for the
coin to make a complete revolution is 1.5 s.
a.
The figure at the right shows the disk and coin as viewed from
above. Draw and label vectors on the figure below to show the
instantaneous acceleration and velocity vectors for the coin
when it is at the position shown. [2]
b.
Determine the speed of the coin. [2]
c.
The rate of rotation of the disk is gradually increased. The coefficient of static
friction between the coin and the disk is 0.50. Determine the speed of the coin
when it just begins to slip. [3]
d.
If the experiment in part (c) were repeated with a second, identical coin glued
to the top of the first coin, how would this affect the answer to part (c)?
Explain your reasoning. [2]
13. A 0.5 kg ball attached to a string which has a length (l) of 0.5 m swings in a
horizontal circle as shown with a constant speed. The string makes an angle  of 15
degrees.
[b] Determine the speed of the ball. [3]
[c] Determine the tension in the string. [2]
14. A bicycle and rider have a combined mass of 95 kg. The bike coasts over the top of a
bridge that has a radius of curvature of 15 meters. The speed of the bike at the peak of
the bridge is 7 m/s. Neglect any frictional effects.
[a] On the diagram above draw a Freebody diagram of all the forces acting on the
bicycle at the location shown. [2]
[b] Determine the magnitude of the force of the hill on the bicycle (and rider) when it
passes over the crest of the bridge. [3]
[c] What is the maximum speed that the bicyclist could travel and not lose contact with
the ground? [2]
Name:
AP Quiz: Circles
C
1-2. A 4-kilogram mass is traveling in a uniform
circular motion at 2 meters per second on a
0.5-meter cord.
1. What is the magnitude of the ball’s
net force?
[a] 4 N
[b] 8 N
[c] 16 N
[d] 32 N
B
A
2. The direction of the acceleration of the object at position B is
[a]
[b]
[c]
[d]
3. Centripetal force Fc acts on a car going around a curve. If the speed of the car were
twice as great, the magnitude of the centripetal force necessary to keep the car moving in
the same path would be
[a] Fc
[b] 2Fc
[c] 0.5 Fc
[d] 4Fc
4. An object with a mass of 0.5 kilogram is swung by a string in a horizontal circle of
radius 1 meter at a speed of 2 meters per second. The magnitude of the acceleration of the
mass is
a) 1 m/s2
b) 2 m/s2
c) 0.5 m/s2
d) 4 m/s2
5. A student on an amusement park ride moves in a circular path with a radius of 3.5
meters once every 8.9 seconds. The student moves at an average speed of
[a] 0.39 m/s
[b] 1.2 m/s
[c] 2.5 m/s
[d] 4.3 m/s
6. The diagram below shows an object moving
counterclockwise around a horizontal, circular track. Which
diagram represents the direction of both the object’s
velocity and the centripetal force acting on the object when
it is in the position shown?
7. A ball of mass M at the end of a string is swung in a horizontal circular path of radius R at
constant speed V. Which combination of changes would result in the smallest centripetal
force acting on the ball?
(1) doubling V and doubling R
(2) doubling V and halving R
(3) halving V and doubling R
(4) halving V and halving R
8.
9. The centripetal acceleration of the satellite is closest to
(1) 9.8 m/s2
(3) 3.2 m/s2
2
(2) 4.9 m/s
(4) 1.6 m/s2
10. A 1.0 × 103-kilogram car travels at a constant speed of 20. meters per second around a
horizontal circular track. The diameter of the track is 1.0 × 102 meters. The magnitude of
the car’s net force is
(1) 200 N
(3) 8000 N
(2) 2000 N
(4) 4000 N
11. The diagram shows the top view of a 65-kilogram student at
point A on an amusement park ride. The ride spins the student in
a horizontal circle of radius 2.5 meters, at a constant speed of 8.6
meters per second. The floor is lowered and the student remains
against the wall without falling to the floor.
a. Calculate the magnitude of the normal force acting on the
student at point A.. [2]
b. Draw a vector that represents the direction of the acceleration of the student at point A
and label is a. Draw a vector that represents the velocity of the student at point A and
label that v. [2]
c. Calculate the minimum coefficient of friction between the student and the wall that
will keep the student from falling. [3]
d. If the student was twice as heavy, how would that affect the acceleration that the
student feels? Explain your reasoning. [2]
12. A ball of mass 0.50 kg is attached to a string and is made to rotate with constant
speed v along a horizontal circle of radius r = 0.33 m. The string is attached to the ceiling
and makes an angle of 300 with the vertical.
a. On the diagram above, draw and label arrows to represent the forces on the ball in the
position shown.
[b] State and explain whether the ball is in equilibrium. [2]
[c] Determine the speed of the ball. [3]
[d] Determine the tension in the string. [2]
.
13. The diagram above shows a 5.0 kg monkey that is going to swing on vine B. When the
monkey reaches the lowest point on vine B it is traveling at approximately 7 m/s.
[a] On the diagram below, draw a freebody diagram showing the forces acting on the monkey
when it reaches the lowest point. Neglect fricitonal effects.
[b]Determine the tension in vine B as the monkey passes through the lowest point of its swing.
[3]
14. Two small blocks, each of mass m, are connected by a string of constant length 4h
and negligible mass. Block A is placed on a frictionless tabletop as shown above, and
block B hangs over the edge of the table. The tabletop is a distance 2h above the floor.
Block B is then released from rest at a distance h above the floor at time t = 0.
a.
In terms of the given quantities and known constants, determine the
acceleration of block B as it descends. [2]
b.
In terms of the given quantities and known constants, determine the tension on
the rope just before B strikes the floor. [3]
c.
Describe the motion of block A from time t =0 to the time when block B
strikes the floor.
d.
Describe the motion of block A from the time block B strikes the floor to the
time block A leaves the table.