Download Chapter_6_AP_Packet

Chapter 6 AP Physics Set
Questions 1 - 2:
A particle moves in a circle in such a way that the x- and y- coordinates of its motion are given in meters as
functions of time t in seconds by:
X = 5 cos (3t)
Y = 5 sin (3t)
1) What is the period of revolution of the particle?
a) 1/3 sec
b) 3 sec
c) 2/3 sec
d) 3/2 sec
e) 6 sec
2) Which of the following is true of the speed of the particle?
a) It is always equal to 5 m/sec.
b) It is always equal to 15 m/sec.
c) It oscillates between 0 and 5 m/sec. d) It oscillates between 0 and 15 m/sec.
e) It oscillates between 5 and 15 m/sec.
3) The radius of the Earth is approximately 6,000 kilometers. The acceleration of an astronaut in a
perfectly circular orbit 300 kilometers above the Earth would be most nearly
a) 0 m/sec2 b) 0.05 m/sec2 c) 5 m/sec2
d) 9 m/sec2
e) 11 m/sec2
4) An automobile of mass m is proceeding around a highway curve of 100 feet radius. The surface of the
roadway is horizontal and the coefficient of friction between the tires and the roadway is 0.50. The
maximum speed with which the car can round the curve without slipping is
a) 10 ft/sec b) 16 ft/sec
c) 32 ft/sec
d) 40 ft/sec
e) 44 ft/sec
5) A highway curve that has a radius of
curvature of 100 meters is banked at an
angle of 150 as shown right.
150
a)
Determine the vehicle speed for which this curve is appropriate if there is no friction between
the road and the tires of the vehicle.
On a dry day when friction is present, a motorcycle successfully negotiates the curve at a speed of 25
meters per second.
b) On the diagram below, in which the block represents the motorcycle, draw and label all of the
forces on the motorcycle.
c)
Determine the minimum value of the coefficient of friction necessary to keep this motorcycle
from sliding as it goes around the curve.
V0
6) An object of mass m moving along the
x-axis with velocity v is slowed by a force
F = -kv, where k is a constant. At time t =0,
the object has a velocity v0 at position x =0,
as shown right.
a)
F = -kv
m
x=0
What is the initial acceleration (magnitude and direction) produced by the resistive force?
b)
v0 --
Derive an equation for the object's velocity as a function of time t, and sketch this
function on the axes below. Let a velocity directed
to the right be considered positive.
--
0
t
c) Derive an equation for the distance the object travels as a function of time t and sketch this
function on the axis below.
x
__
__
0
t
d) Determine the distance the object travels from t = 0 to t = .
7) A car of mass m, initially at rest at time t = 0,
is driven to the right, as shown, along a straight,
horizontal road with the engine causing a constant
force F0 to be applied. While moving, the car
encounters a resistance force equal to -kv, where
v is the velocity of the car and k is a positive
constant. to the right.
a)
v
The dot below represents the center of mass of the car. On this figure, draw and label vectors to
represent all the forces acting on the car as it moves with a velocity v to the right.
b) Determine the horizontal acceleration of the car in terms of k, v, F0, and m.
c)
Derive the equation expressing the velocity of the car as a function of time t in terms of k, F0, and
m.
d) On the axes below, sketch a graph of the car's velocity v as a function of time t. Label important
values on the vertical axis.
v
0
e)
t
On the axes below, sketch a graph of the car's acceleration as a function of time t. Label important
values on the vertical axis.
a
0
t
8) A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive
force caused by the air). The drag force on the ball has magnitude bv2, where b is a constant drag
coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional
to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the
ball. As the ball falls, its speed approaches a constant value called the terminal speed.
a)
On the figure below, draw and label all the forces on the ball at some instant before it reaches
terminal speed.
b) State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or
remains the same as the ball approaches terminal speed. Explain.
c)
Write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in terms
of time t, the given quantities, and fundamental constants.
d) Determine the terminal speed vt in terms of the given quantities and fundamental constants.
e)
Determine the energy dissipated by the drag force during the fall if the ball is released at height h
and reaches its terminal speed before hitting the ground, in terms of the given quantities and
fundamental constants.
9) A small rocket is fired vertically from the Earth's surface and ascends with a constant vertical
acceleration of 80 ft/sec2 for 60 seconds. The fuel is then all expended and the rocket continues as a
free particle. Air friction is negligible.
a)
Find the maximum height above the firing point reached by the rocket.
b) Will the time for its descent back to the Earth's surface be longer than the time for its ascent? Give
reasons.
10) A small block of mass m slides on a horizontal
frictionless surface as it travels around the inside of a
hoop of radius R. The coefficient of friction between the
block and the wall is ; therefore, the speed v of the block
decreases. In terms of m, R,  and v, find expressions for
each of the following:
a)
The frictional force on the block.
b) The block's tangential acceleration dv / dt
c)
The time required to reduce the speed of the block from an initial value v0 to 1/3 (v0).
11) A ball of mass M attached to a string of length
L moves in a circle in a vertical plane as shown right
at the top of the circular path, the tension in the string
is twice the weight of the ball. At the bottom, the
ball just clears the ground. Air resistance is negligible.
Express all answers in terms on M, L and g.
a) Determine the magnitude and direction
of the net force on the ball when it is at the top.
b) Determine the speed v0 of the ball at the top.
The string is then cut when the ball is at the top.
c)
Determine the time it takes the ball to reach the ground.
d) Determine the horizontal distance the ball travels before hitting the ground.
M