Download Chapter_6_In-class_problems_(section_by_section_notes)

Chapter 6, Section 1A: IN-CLASS Examples
1. A 2000 kg car is driving at 30 m/s on a flat road. The maximum coefficient friction
between the car’s tires and the road is 0.8. Find the maximum stopping acceleration of the
car if the brakes are suddenly “slammed on”. Give your answer in variable form and as a
numerical answer.
2. A 2000 kg car hits a set of woop-de-doos in the road, as shown below. He maintains a
constant speed of 30 m/s during the entire trip. The bump in the road is part of a circular
arc of radius 100 meters while the dip in the road is a part of a circular arc of radius 150
meters. In both variable form and as a numerical answer, find…
a) the apparent weight of the car at the top of the bump.
b) the apparent weight of the car at the bottom of the dip.
3. The same 2000 kg car hits the same set of woop-de-doos from the previous problem. The
maximum coefficient of friction between his tires and the road is again 0.8. Unfortunately
for the driver, a small cat is standing on the backside of the hill. He can’t see this cat until
he reaches the top of the hill. If he crests the hill at 30 m/s and immediately slams on his
brakes, find the ….
a)
b)
c)
d)
centripetal acceleration of the car.
tangential acceleration of the car.
total acceleration of the car.
“braking” acceleration of the car (the acceleration that is slowing the car down so that it
can avoid hitting the cat)
4. A ball of mass 80 grams is swung on a string of length 75 cm in a vertical circle. Assume
that an angle of 0o is formed between the string and the vertical when the ball is at its
lowest possible position. If the instantaneous speed of the mass is 20 m/s, find the tension
in the rope and the total acceleration of the mass at the moment that the string makes an
angle of …
a) 40o with the vertical.
b) 140 o with the vertical.
5. A jet pilot is sitting on a scale. The scale reads 1000N as he coasts through the air.
Suddenly, and without warning, he is attacked by an enemy jet. In an evasive maneuver, he
puts the jet into a death-defying nose-dive. In order to avoid a horrific crash, the pilot pulls
up hard on the stick, causing the plane to fly in a concave upward circular path of radius
2000 m. At a certain instant in time, the jet’s speedometer reads 300 m/s and his scale
reads 5000N. Find the angle between the back of the pilots seat and the vertical at this
instant in time.
6. In the previous problem, it is assumed that the pilot’s head was constantly pointing inward,
towards the center of the circle. This is much more safe than a circular loop where the
pilots head points out of the circle. Explain why?
Chapter 6, Section 1A/2: IN-CLASS Examples
1. A certain conical pendulum on the surface of the moon (where the acceleration due to
gravity is 1/6th of the acceleration due to gravity on the Earth’s surface) consists of a 30
gram mass on a 70 cm long string. The mass revolves around a horizontal circle of radius
40cm at a constant speed. Find the speed of the mass as well as the angle made between the
string and the vertical.
2. A 1000 kg car traveling on a banked turn of radius 150 meters with a coefficient of friction
of .3 between the wet road and the wet tires is traveling at 30 m/s when it starts to slip and
move UP the incline. Find the angle of the embankment.
3.
For the car in problem #2 on the previous page, find the speed that the car can travel
around the turn so that any excess tire wear is avoided.
4. A ball of mass 1 kg is swung on a string in a vertical circle of diameter 2 meters. At any
given moment of time, assume that the speed of the ball is 9 m/s. Find the tension in the
string, as well as the total acceleration of the mass, at …
a)
b)
c)
d)
the top of the circle.
the bottom of the circle.
the side of the circle.
30o above the lowest point, moving upward.
Chapter 6, Section 3
Newton’s 1st Law
An object in motion or at rest will remain in motion or at rest unless acted
upon by an unbalanced, external force.
OR
If an object does not interact with other objects, it is possible to identify a
reference frame in which the object has zero acceleration.
 huh ????
INERTIAL FRAME OF REFERENCE: A reference frame in which an
object does NOT have an acceleration.
Any frame of reference that moves with a constant velocity relative to an
inertial reference frame is also an inertial reference frame.
Although our current location on the earth’s surface is accelerating, we
will assume that the earth is at rest, thus being an inertial frame of
reference.
When a frame of reference is accelerating, this is called a NONINERTIAL frame of reference.
“Unexplained” accelerations, and thus forces (MYSTERY FORCES!?!),
are characteristic of NON-INERTIAL frames.
Chapter 6, Section 4
Slow moving falling object (thru oil, shampoo, water, etc)
mg
R  bv
vT 
b
b  proportion ality constant
 bt
mg  mg

v

 v1 e m
b  b

ag
b
v
m
Fast moving falling object (through air, etc)
R  kv2
k
1
DA
2
vT 
mg
k
ag
k 2
v
m
k = proportionality constant
D = drag coefficient
 = density of medium
A = cross-sectional area of object (area of the front of the object that falls through the medium)
Some useful information to get through the HW problems 
Density Table
g/cm^3
water
1.00
aluminum
2.70
zinc
7.13
iron
7.87
copper
8.96
silver
10.49
lead
11.36
mercury
13.55
gold
19.32
Air (rm temp) .0012
* Note: You must use units of cm with densities of g/cm3, and then you must convert
the end.
g to kg at
Chapter 6, Section 4: IN-CLASS Examples
1. A child slide on a sled across an icy surface at an initial speed of 4 m/s. The
friction (due to the ice and to air resistance) is given by F f = - 1/4kmv2 ,
where “k” is a constant of magnitude 0.4 and “m” is the 70 kg mass of the
child and the sled. Find the velocity of the child/sled after 2 seconds.
(Make sure to derive all equations that you use)
2. An aluminum sphere of radius 80cm is dropped from an airplane. If the drag
coefficient on the sphere is 0.6, find …
a) the terminal velocity of the sphere.
b) the resistive force acting on the sphere at the 3 second mark.
c) The sphere’s acceleration after 2 seconds.
3. A rectangular block of mass 200 grams is dropped thru an oily liquid. It
reaches a terminal speed of 8 cm/s. Find…
a. the acceleration of the block after 1 sec.
b. the resistive force on the block after 1 sec.
4. A 300 gram hockey puck is given an initial speed of 40 m/s. If the resistive
proportionality constant of the air is .08, the ice is assumed frictionless, and
the resistive force is proportional to the pucks velocity, find…
a. the speed of the puck after 6 seconds.
b. the time needed for the puck to reach ¼ of its initial speed.