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Part 2
Motion
65
Motion
Speed
Speed, is a measure of how fast an object is moving. Just like with your speedometer on
your car, it tells you how far you are traveling in how much time. For example, your
speedometer tells you how many miles you travel in one hour.
Velocity
Velocity is similar to speed. It is a measure of how fast an object moves, or how fast the
distance changes. The difference between speed and velocity is that for speed you do not care
what direction you are going, it only matters how fast. Velocity, on the other hand, is a two-part
quantity. To be able to tell me your velocity, you need to tell me how fast you are going (your
speed) and tell me what direction you are going. For example, an airline pilot cares about the
velocity of his plane - he cares not only about how fast he is going, but also that he is going the
right direction to the airport. Velocity is abbreviated with a small v. In the equation below,
distance is abbreviated by a capital D, and time is abbreviated by a small t.
Any quantity that needs both a size and a direction to describe it is called a vector.
D
v
t
Plus direction!!
The circle above is a way to solve this formula for any one quantity. Just cover-up the
quantity you want, and the other two will be in the positions you need for the solution. For
example, if you cover up the ‘v’ in the circle, you have ‘D over t’ - just like the formula next to
the circle above.
The equation above also shows what the proper units are for a velocity is a distance
divided by a time. Your speedometer shows you your speed in miles per hour (mi/h), and in
kilometers per hour (km/h).
Example 1
A truck averages 50 mph. How far does it go in an 8 hour day?
In this problem v = 50 mi/h and t = 8 h. (note: we are accustomed to seeing ‘mph’ to
abbreviate ‘miles per hour’. It works best in calculations to write this as ‘mi/h’, which is the
same as
mi
.)
h
Look at the circle above, and cover-up the ‘D’, and you are left with ‘v’ and ‘t’ next to
each other, which means ‘v times t’:
D=vt
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Example 2
Seattle is 160 miles away. How long will it take to get there if you average 60 mi/h?
In this problem v = 60 m/h and D = 160 miles.
Using the circle at right, and covering up the ‘t’, you get ‘D over v’.
t
D
v
Acceleration
Acceleration is a measure of how quickly velocity changes. If you are speeding up you
have a positive acceleration, what we generally think of as ‘accelerating’. However, you can
have a negative acceleration - this is the case if you are slowing down. This is sometimes called
deceleration. But don’t get confused, an acceleration can be either negative or positive - a
speeding up or a slowing down. From this you can get the idea that the direction of the
acceleration makes a difference, as shown by the positive and negative part. This means that
acceleration is a vector, and to be complete, we must give the direction of the acceleration. This
can be done by giving a direction (for example, North, or Up) or by comparing to the direction of
the velocity (for example, positive or negative, speeding up, or slowing down).
Acceleration = velocity change / time
in shorthand notation, where acceleration is abbreviated by a small a,
v
a
t
The units of an acceleration are a distance unit divided by two time units. For example if
the velocity changed by 10 m/s in 1 s, the acceleration would be 10 m/s/s or 10 m/s2.
Example 3
A sports car goes from 30 mph (44.1 ft/s) to 40 mph (58.8 ft/s) in 2.3 seconds.
What is the average acceleration?
In this problem the change in velocity, v = 58.8 ft/s – 44.1 ft/s = 14.7 ft/s and the time t = 2.3 sec
thus
ft
v
s  6.4 ft .
a 
t
2.3s
s2
14.7
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Example 4a
A ball is dropped off of a building. How fast is it going after falling 2.7 sec? (Hint the
acceleration of free fall is 10m/s2).
In this problem a = 10m/s2 and t = 2.7 s. The speed can be found using v = at.
v = 10m/s2 x 2.7 s = 27 m/s
Vf or average V? That is the question!
In problems with acceleration, the velocity is changing, so we must be careful about what
we mean by the symbol ‘v’. As an example, suppose on a trip from Vancouver to Salt
Lake City (about 750 mi), you start out at 7 AM on Saturday, and maintain a speed of 75
mph on the freeway. You stop for lunch, and, feeling tired, decide to stay the night in
Boise before driving on. The next morning you start out at 7AM, maintaining a speed of
80 mph and arrive in Salt Lake at 1 PM (Vancouver time, you haven’t reset your watch)
At various times during the trip, your speed was 75 mph, 80 mph and 0 mph. Overall,
you took 30 hours to travel 750 mi for an average speed of 25 mph (750 mi/30 hrs). So
we need to talk about these various velocities.
Generally, the symbol ‘v’ is used for the velocity at a particular time, such as that on your
speedometer. so, in example 4, the ball dropped from the building has a velocity of
27 m/s downward at the moment 2.7 sec after release. This is the instantaneous velocity
and is the one involved in the relations
and
The average velocity is equal to the total displacement divided by the total time taken, as
in the example road trip. If an object accelerates at a constant rate, there is another way
to calculate the average velocity. In this case you can calculate average velocity the same
way you would the average of any two numbers; add them and divide by two. The two
numbers to add are the initial and final velocities.
vave 
vi  v f
2
Since this average velocity is equal to the total distance traveled divided by the total time taken,
the distance can be found using D = vavg t .
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Example 4b
A ball is dropped off of a building. How far does it fall in 2.7 sec?
(Hint the acceleration of free fall is 10m/s2). From 4a, vf = 27 m/s
v ave 
vi  v f
2
or vave 
m
s  13.5 m
2
s
0  27
Now, D = vavg t = 13.5 m x 2.7 s = 36.45 m
s
Example 5
A drag racer goes a quarter mile in 6.9 sec. If the acceleration is uniform what was the top speed?
The distance D is 1320 ft (there is 5280 ft in 1 mile, so we want one quarter of that).
The time, t= 6.9 sec. You can use the formula v avg 
vavg 
D
to find the average speed.
t
D 1320 ft
ft

 191
t
6.9 s
s
This is the average speed. If you look at the equation above for the average velocity, you can see
that if the car started from rest, then vi is zero. This leaves us with the top speed is just twice this
2 x 191 ft/s = 383 ft/s.
Converting to miles per hour
383 ft/s x (1 mi/h / 1.47 ft/s) = 260 mi/h
WARNING: BRAIN CRAMPS AHEAD!!
One more comment about speed. So far, we have simply used speed as the size of the velocity.
Velocity has a size (how fast, or speed) and a direction. There are contexts where speed and
velocity can have no relation at all!!
Consider a stock car race where the cars run 20 laps around a closed track, fastest vehicle wins.
Well, fastest means the one with the highest speed. So the car which takes the least amount of
time to complete 20 laps is the fastest. If each lap is one mile, then the car’s speed can be
determined by the total distance (20 mi) divided by the time it took, say 15 min.
So, the winning speed would be:
20 mi | 60 min = 80 mi = 80 mph
15 min | 1 hr
hr
But this isn’t at all related to the average velocity of the car!!! This may be a good estimate of
the size of the instantaneous velocity of the car (speedometer reading), but the direction is always
changing. The total distance traveled on the track is 20 mi. but the total displacement (net
distance from starting point to ending point) is zero; it ended up where it started!!!! In this case,
the average velocity would be the total displacement divided by the total time, or zero divided by
15 min. = 0 !!
I discuss this here only as a matter of completeness, we will avoid such oddities with closed loop
paths and different displacement and distance traveled as much as possible in this course.
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Laws of Motion
A force is something that causes motion - a push or a pull. Since it matters what
direction the push or the pull is we can tell that a force is a vector. Force is abbreviated by a
capital F.
In the American system, force is measured in pounds (lb). In the metric system it is
measured in Newtons (N). There are about four and one-half N to a lb.
Most of the time there are many forces acting on an object at one time. This book is
being pulled on by gravity, and the table it rests on is pushing back. A skydiver will have the
force of gravity pulling him down, and the wind resistance slowing him down. The skydiver will
continue to speed up until the push of the wind equals the force of gravity.
The net force is the force left over after all cancellations of forces in opposite directions
have taken place. This net force is what can make a change in the motion of an object. During
the time that the force of gravity on the skydiver is larger than the wind resistance, there is a net
force downward on the diver, and he will continue to speed up.
There are three laws that describe how forces affect the motion of objects - Newton’s
three laws:
Newton's 1st Law
An object at rest will remain at rest. An object in motion
will remain in motion going at constant speed in a
straight line (in the absence of a net force).
If there is a zero net force, then the velocity does not
change.
Newton's 2nd Law
The greater the net force on an object, the greater the
acceleration of the object. The greater the mass
(abbreviated with a m) of an object, the more force is
needed for a given acceleration.
F = ma
Newton's 3rd Law
For every force there is an equal and opposite force.
Weight (W) is the force on an object due to gravity. It is computed using the
acceleration of gravity (g) which is 10 m/s2 metric or 32 ft/s2 American.
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W = mg
m = W/g
m (American) = W (lb) / 32 ft/s2
Friction
Friction is a complicated and inexact field of physics, but still there is a lot known about it.
There are three types of friction:
1.
static (objects at rest)
2.
kinetic (objects moving)
3.
rolling
Static friction is normally greater than kinetic and rolling friction. Rolling is usually the
least. The amount of friction normally depends only on the nature of the surface.
Area makes no difference as long as the nature of the surfaces does not change. If the
area is made so small, and the surface melts or scratches, then the friction will change.
The coefficient of friction, , is used to figure out the amount of friction. It is defined as

F
, where F is the force to pull the object, and W is the weight
W
If the coefficient of friction is known then force can be computed. The following table
gives examples of static, kinetic, and rolling frictional coefficients of common objects.
Object and Surface
s
k
wood on wood
0.5
0.3
wood on stone
0.5
0.4
steel on steel (smooth)
0.15
0.09
metal on metal (lubricated)
0.03
0.03
rubber tire on dry concrete
1
0.7
rubber tire on wet concrete
0.7
0.5
steel wheel on steel rail
r
0.04
0.0045
Example
Calculate the force needed to push a 3000 lb auto once it is moving.
This is a rolling tire, so  = 0.04 from the table.
F =  w = 0.04 x 3000 lb = 120 lbs
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In stopping, applying the brakes slows the rate of rotation of the tires, so they begin to drag on the
road. If this is just a slight drag, the friction is like that of a static tire not sliding across the
pavement. If you lock the wheels and skid, the friction is kinetic friction of tires sliding on the
road. Notice how there is more friction in stopping by not skidding. Also note that the weight of
the car does not affect the coefficient. Everything else equal, large and small vehicles take about
the same distance to stop.
Whenever you have friction, heat is developed.
Conclusion: Friction depends on the surfaces and not, to a large
extent, on the speed and area.
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Work – Energy
We have already used the idea of work in analyzing machines. Here we will give a more formal
discussion. The definition of work involves two quantities and a condition. The quantities are
force and distance (or motion). The condition is the force (or some of it) must be in the same
direction as the motion.
Work = force x distance
Work
F
Work = FD, same direction or opposite.
D
Thus, if you lift a 40 lb transmission 2 feet, you do 40 lb x 2 ft = 80 ft-lbs of work. However, if
you just hold a transmission 2 ft off the floor without moving it, you do no work on the
transmission, because the transmission must move through a distance for work to be done. The
energy you expend as you get tired is in small muscle motions within your arms, etc. which is
work resulting in waste heat (and aches and pains).
Which of the following involves doing work on an object?
1.
lifting a suitcase
4.
pulling a wagon
2.
carrying a suitcase
5.
climbing stairs
3.
pushing a wagon
6.
holding a bow taut
In the metric system W = Newtons x meters = joules (J)
Energy may be defined as the ability to do work. There are many kinds of energy.
1.
gravitational potential energy (height) 5.
electrical energy (electric charges)
2.
kinetic energy
6.
nuclear energy (nuclear particle changes)
3.
elastic potential energy (springs)
7.
heat energy (friction, random motion)
4.
chemical energy (food, batteries)
Gravitational Potential Energy (PE) is the energy stored up when you do work lifting an object to
a certain height (energy of position).
PE = W x h = m x g x h
Kinetic Energy (KE) is the energy due to an object’s motion.
KE = (1/2) x m x v x v = (1/2) x m x v2
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There is a law sometimes called the law of conservation of energy that says that you can't get
more out of a system than you put into it. For example the energy to make a truck go comes from
the fuel used. Your energy comes from the food you eat. In the case of an automobile, the chain
of energy transformations looks something like this:
Fuel containing
chemical energy
Most of the original energy
of the fuel is lost as heat
throught the exhaust and
cooling system.
Combustion chamber where
chemical energy is converted
to heat energy.
The wheels do work by
pushing on the road making
the vehicle move.
Heat energy does work by
pushing down on piston.
W = F xd
This work is transmitted
to the wheels through the
drive chain.
Remember from our discussion of machines that, for each transformation in the real world, there
will be an energy loss, which generally goes directly to waste heat.
Power
Power is defined as work divided by time. Power is abbreviated with a capital P.
P
Work
t
In other words, if one motor does 100 ft-lbs of work in 6 seconds and another does the same
amount of work in 12 seconds, the first is twice as powerful even though they did the same
amount of work.
P = Work / t = 100 ft lb / 6 s = 16.7 ft lb/s
P = Work / t = 100 ft lb / 12 s = 8.33 ft lb/s
P = Work / t = 100 J / 10 s = 10 watts (W)
Power can be measured in horsepower or watts, or ft lb/s.
1 hp = 550 ft lb/s = 746 W
Example
A 140 lb person climbs 15 vertical ft. up a stairway in 2.4 sec.
Find the power in horsepower and Watts.
P = Work / t = F x d / t = 140 lb x 15 ft / 2.4 s = 875 ft lb/s
875 ft lb/s x 1 hp/(550 ft lb/s) = 1.59 hp
875 ft lb/s x 1.36 W/ (ft lb/s) = 1190 W
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Torque and power:
Many people confuse power and force or torque. For example, if one puts a reduction gear on a
drill it does not make the drill more powerful. It does increase the torque, but there is a price –
reduced speed.
You never get something
for nothing!!
+
Torque
Torque is essentially a rotational force. A torque acts to change the rotation rate of an object just
as a linear force acts to change the velocity of an object.
F
r
Example 1
20 lbs
1 ft
10 lbs
1 ft
A
B
A has more torque than B since the force is greater in A.
Example 2
20 lbs
20 lbs
1 ft
3 ft
A
B
A has more torque since the distance from the turning point (axle) is greater.
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The amount of torque is equal to the product of the lever arm and the right angle force.
T=LxF
Force
Lever Arm
Example 3
10 lbs
Torque = 10 lb x 2 ft
= 20 lb ft
2 ft
Example 4
50 lbs
T=50 lb x 3 in = 150 lb–in
or
3 in x (1 ft / 12 in) = .25 ft
T = 50 lb x .25 ft = 12.5 ft lb
3 "= radius
If you pull at an angle other than 90° the
torque is not as much since the lever arm is
shorter.
If you use an extension on the handle of the
wrench the torque is greater because the lever
arm is longer.
While we are on the subject of rotational motion, there is a quantity which plays the same role in
rotation as mass does in linear motion. In motion, the inertial mass is essentially the resistance of
an object to acceleration ( a = F/m). The more mass, the more force required to achieve a given
acceleration.
In rotational motion, the distribution of the mass also makes a difference. When an object rotates,
it does so about an axis (like the center of an axle for a wheel). It turns out that the farther the
mass is from the axis of rotation, the more it resists changes in rotation rate.
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A common use of this is the flywheel, used in many situations to store energy.
Some experimental cars have used flywheels to store energy from
braking (the wheels are connected to the flywheel for braking: the slower
flywheel resists speeding up and causes a drag on the wheels, the wheels
transfer energy to the flywheel through the coupling). This energy can
then be used to accelerate the car by coupling the flywheel to the drive
system on start-up.
To be most effective, the flywheel has most of its mass on the outside
rim, giving it more rotational inertia.
In the other direction, in order for pulleys to have as little effect as possible on the rotation rate of
a belt, they should have as little mass as possible out towards the rim. Many of our more ideal
pulleys in the lab have holes cut through the disk to decrease the amount of mass far from the
rotation axis.
MOTION
Distance
Velocity
Time
Acceleration
Change in velocity
D
v
(d)
(v)
(t)
(a)
(v)
vave 
vi  v f
2
vavg = d total / t total
v
t
a
t
Friction coefficient:

F
W
Circular Motion:
Torque: T = r x F
Energy, work:
Gravitational Potential Energy : PE = W x h = m x g x h
Kinetic Energy (energy of motion): KE = (1/2) x m x v x v = (1/2) x m x v2
Work
F
D
Power : P 
Work
t
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Exercises
Velocity Review
1.
The piston travels from a distance of 6 in, in 0.16 seconds. What is the average speed of
the piston during this time in ft/s ?
Average speed = ____________
2.
Change your answer to question 1 into miles per hour and meters/s.
Average speed = ____________ mi/h
__________ m/s
3.
A jet can travel with an average air speed of 500 mi/hr. How far can it go in 9.5 hours at
this speed?
distance = ______________
4.
A drag racer completes the 1/4 mile in 6.8 seconds. What is the average speed of the car
in ft/sec and mi/hr?
Average Speed = ____________ = ____________
5.
Assuming the dragster accelerated from rest to his final speed uniformly. What would his
final speed be if his average speed was 150 mi/hr?
final speed = __________________
6.
A runner runs around a 1/4 mile track in 60 sec. What is her average speed?
Average speed = ______________
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Acceleration Review
1.
As an object freely falls, its
a.
velocity increases.
b.
acceleration increases.
c.
both of the above.
d.
none of the above.
2.
If a freely falling object were somehow equipped with a speedometer, its speed reading
would increase each second by about
a.
6 ft/s.
b.
32 ft/s.
c.
48 ft/s.
d.
a variable amount.
e.
depends on its initial speed.
3.
If a freely falling object were somehow equipped with an odometer to measure the
distance it travels, then the amount of distance it travels each succeeding second would be
a.
constant.
b.
less and less.
c.
greater than the second before.
4.
An object travels 8 meters in the first second, 8 meters in the second second, and 8 meters
again during the third second. Its acceleration is
a.
0 m/s2
b.
8 m/s2
c.
16 m/s2
24 m/s2
d.
e.
5.
none of these.
Ten second after starting from rest a freely falling object will have a speed of about
a.
32 ft/s.
b.
160 ft/s.
c.
16 ft/s.
d.
320 ft/s.
e.
none of these.
6.
Two seconds after starting from rest a freely falling object will have traveled a total
distance of
a.
16 ft.
b.
32 ft.
c.
48 ft.
d.
64 ft.
e.
none of these.
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7.
A car accelerates from rest at 2 ft/s2. What is its speed 4 sec later?
a.
2 ft/s
b.
4 ft/s
c.
6 ft/s
d.
8 ft/s
e.
none of these
8.
A bullet is fired straight down from the top of a building. Neglecting air resistance, the
acceleration of the bullet is
a.
less than 10 m/s2
b.
equal to 10 m/s2
c.
d.
greater than 10 m/s2
more information is needed to determine.
9.
A car starts from rest and accelerates at a constant rate of 32 ft/s2. How fast will the car
be going in
a.
0.5 sec?
b.
1.0 sec?
c.
4.0 sec?
10.
a. When you drop a rock, how fast will it be falling after 1.0 sec?
speed = ________________ m/s
b. What is the rock’s average speed for the time from 0 to 1.0 sec?
average speed = _____________ m/s
c. How far does the rock fall in the first 1.0 sec?
distance = _____________ m
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11.
You are traveling down the road at a speed of 88 ft/sec and slam on your brakes.
If the brakes give your car a deceleration of 11 ft/s2.
a.
How long will it take you to stop?
time = ________________
b.
What is your average speed while you are stopping?
average speed = _________________
c.
How far will your car move while you are stopping?
distnace = _______________
Force Review
1.
When the net force acting on an object doubles, the acceleration
a.
quadruples.
b.
doubles.
c.
remains the same.
d.
halves.
e.
none of these.
2.
An object is accelerated through space (someplace that there is no friction) by a net force
f. If the weight doubles, its acceleration will
a.
quadruple.
b.
double.
c.
stay the same.
d.
half.
e.
none of these.
3.
The force of friction on a sliding object is 10 lbs. The force needed to maintain a constant
velocity is
a.
more than 10 lbs.
b.
less than 10 lbs.
c.
just 10 lbs.
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4.
Fill in the table below
Force (N) =
10
5
5
20
50
100
1
10
10
10
=
=
=
=
=
=
=
=
=
=
Mass (kg)
10
10
Acceleration
(m/s2)
1
10
1
50
50
2
0.5
Force
Mass
Accel eration
The above results can be summarized in equation form by F = ma
5.
A total force of 50 lbs is applied to a 32 lb object. What will be the acceleration of this
object?
acceleration = ______________
How fast will it be moving at the end of 3.0 sec?
speed = ____________________
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6.
An object accelerates at a rate of 4.0 ft/s2 when a force of 16 lbs is applied. What is the
weight of the object?
Weight = __________________
7.
How much force is required to accelerate a 96 lb object at a rate of 10 ft/s2?
Force = __________________
Work – Energy Review
1.
A 1000 kg car and a 2000 kg are hoisted the same distance up in a gas station. Raising the
more massive car requires
a.
less work.
b.
as much work.
c.
twice as much work.
d.
four times as much work.
e.
more than four times as much work.
2.
When an object is lifted 10 meters, it gains a certain amount of potential energy. If the
same object is lifted 20 meters, its potential energy is
a.
less.
b.
the same.
c.
twice as much.
d.
four times as much.
e.
more than four times as much.
3.
Which requires more work lifting a 50 kg sack 2 m or a 25 kg sack 4 m?
a.
lifting the 50 kg sack.
b.
lifting the 25 kg sack.
c.
both require the same amount of work.
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4.
A man lifts a box that weighs 20 lb a distance of 3.0 ft. How much work does the man do
in lifting the box?
a.
6.66 ft–lb
b.
60 ft–lb
c.
23 ft–lb
d.
5 ft–lb
e.
none of these
5.
A car traveling at 40 mph slams on his brakes and skids to a stop in 100 ft. If the same car
is traveling at 80 mph, how far will it skid when it slams on the brakes?
a.
100 ft
b.
200 ft
c.
300 ft
d.
400 ft
e.
none of the above
6.
Car A has a weight of 1000 lbs and a speed of 60 mi/hr. Car B has a weight of 2000 lbs
and a speed of 30 mi/hr. The kinetic energy of car A is
a.
half that of B.
b.
equal to that of B.
c.
twice that of B.
d.
four times that of B.
7.
1 HP is equal to
a.
550 ft-lb/sec.
b.
746 watts.
c.
0.746 kilowatts.
d.
2550 BTU/hr.
e.
all of these.
8.
The power required of a motor to raise 550 lb 1 ft into the air in 10 seconds is
a.
1 hp.
b.
0.1 hp.
c.
10 hp.
d.
100 hp.
e.
none of these.
9.
How many kilowatt hours of energy are used up while burning ten (10) 100 watt lightbulbs for 10 hours?
a.
10
b.
100
c.
1000
d.
10,000
e.
none of these
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10.
day?
At $0.04 per kilowatt hr how much does it cost to run a 2000 watt heater for 10 hours a
a.
b.
c.
d.
e.
f.
20 cents
40 cents
60 cents
80 cents
$1.00
none of these
11.
How many ft lb/sec of power are needed to raise a 200 lb object 20 ft in the air in 5 sec?
a.
4000
b.
2000
c.
1000
d.
800
e.
400
f.
none of these
12.
How much work is required to lift five 200 lb people 50 ft in an elevator?
Work = ____________
13.
You can buy about 27 kilowatt hours of electric energy for $1.00.
a.
If all of this energy was converted into work how many ft-lbs of work would be
done for $1.00?
Work = _________
b.
If this work was used in raising water up 100 ft how many lbs of water can be
raised for $1.00?
Weight = _________
c. Water weighs 8.3 lbs per gallon. How many gallons of water can be raised for $1.00?
Volume = _________
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14.
Diesel fuel contains about 120,000,000 ft-lb of chemical potential energy for each gallon.
a.
If 1 gallon of diesel was used in a motor that is 20% efficient to run a water
pump, how many lbs of water could be raised 100 ft in the air?
Weight = ______________
b.
How many gallons of water is this? (1 gallon of water weighs 8.3 lbs)
Volume = ____________
c. If this energy was consumed in 0.5 hr, what was the power consumption of the motor?
Power used = __________
d.
What would be the power delivered by the motor?
Power delivered = __________
Torque Review
1.
A torque acting on an object at rest tends to produce
a.
equilibrium.
b.
rotation.
c.
velocity.
d.
a center of gravity.
2.
The maintenance manual of a Datsun requires that the head bolts be tighten down with a
torque of 120 ft–lb. If you are using a wrench that has a 6 in handle, what force must you supply
to the end of the wrench?
a.
60 lb
b.
120 lb
c.
180 lb
d.
240 lb
e.
none of these
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3.
What is easier to rotate? A 10 kg mass shaped like
a.
a hula hoop of radius R about an axis through the center of the hoop and
perpendicular to the plane of the hoop.
b.
a disk of radius R about an axis through the center of the disk and perpendicular
to the plane of the disk.
c.
a solid cone with base of radius R about an axis through the center of the cone
and perpendicular to the base.
4.
The rotational inertia of your body is greatest when you are
a.
standing tall.
b.
tucked.
c.
same either way.
5.
Assume the force, F, in each picture below has the same magnitude, but acts in the
direction shown. In which position will the torque applied to the crankshaft by the piston be the
greatest?
a.
b.
c.
d.
Rotational Motion Review
1.
Suppose you put very large tires on your car. Then your speedometer will read
a.
b.
c.
2.
high.
low.
actual speed of the car.
One horse on a merry go round is 4 ft from the center and moves with a linear
speed of 10 ft/s. Another horse that is on the same merry-go-round at a distance of
6 ft from the center will be traveling at
a.
b.
c.
d.
e.
10 ft/s.
15 ft/s.
20 ft/s.
25 ft/s.
30 ft/s.
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3.As the rotational speed of a space habitat increases the weight of the occupants
a.
b.
c.
4.
In using a strobe light to measure the rotational speed of a fly wheel you find that a
scratch on the fly wheel is made to stand still at a rpm flash rate of 100 rpm, 200
rpm, and 300 rpm. However at 600 rpm you see two images of the scratch
separated by 180 degrees. The real rpm of the wheel is
a.
b.
c.
d.
e.
5.
increases.
decreases.
stays the same.
100 rpm.
200 rpm.
300 rpm.
600 rpm.
not enough information given.
Centrifugal forces are an apparent reality to observers in a reference frame that is
a.
b.
c.
d.
e.
moving at constant velocity.
an inertial reference frame.
at rest.
rotating.
none of these.
6.
If the distance from the center of a propeller to the outer edge is 2.0 ft, how fast
will an atom on the tip of the propeller be moving when the propeller rotates at
4000 rpm?
7.
A fly-wheel is rotating at 3000 rpm. How many revolutions per second is this?
How long does it take to complete 1 revolution?
8.
What keeps the Earth moving in a nearly circular path about the sun?
9.
The Earth is 93,000,000 miles from the sun and it takes 365 days for it to complete
one revolution. From this find the speed, in miles per hour, of the Earth as it goes
around the sun. (Remember 365 days is 365 x 24 hours.)
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