Review for Physics I final (Answers
to problems)
(The
answers to these problems were worked quickly and not checked so may contain
errors. If you find any errors please
email me. The velocity on one problem
was missing, it is included below. We
will discuss these problems Monday and Tuesday)
Review
for Physics I final Fall
2007
Final will be 8 AM,
Wednesday, December 5. Students who wish
to do so may begin their final exam at
You may bring to the final
one 8” x 11" page which may be written on both sides. There are no restrictions on what you put on
the sheet.
Be able to state in complete
and comprehensible English sentences the principles of physics as applied to
specific problems. Just writing
“conservation of energy” or “vertical motion is independent of horizontal
motion” will get you less than half credit on questions of this type. Your statement should be of the type “The
kinetic energy of the pendulum just after the ball strikes it will be equal the
potential energy of the pendulum at the top of its swing. The assumption is that the entire mass of the
pendulum is at the position of the ball at the end of the pendulum.”
Know what the principles of
the conservation of linear momentum, angular momentum and energy tell us about
the laws of physics in space and time.
Be able to draw clearly
labeled diagrams including free body and net force diagrams.
Be able to show clearly all
the steps in the solution of all problems.
Topics for the final exam -
You are certain to have at least one problem from the following areas:
Conservation
of energy (including the work-energy theorem, rotational motion and heat energy
problems with heats of evaporation and fusion)
Conservation
of (linear and angular) momentum
Vectors:
addition, subtraction
Rectilinear
motion - velocity, acceleration, f = ma, friction
Elastic
and inelastic collisions
Projectile
motion
Selected problems from the
following areas will also be on the final.
Gravity - weightlessness,
(orbital motion)
Rotational motion -
centripetal force - moment of inertia – (torque - center of gravity)
Vector products (dot product,
cross product)
Statics
The above list does not
include all possible problems but the overwhelming majority of problems will be
from these areas. The tests we had are
an indication of what is most important.
Be sure you are able to work and completely understand all the problems
from our tests.
Practice problems: To benefit from these problems, show your
statement of the principle and your solution to Dr. Gault. Answers are available upon request.
A 220 lb man is sitting
beside his 140 lb girlfriend in her Ferrari holding a protractor that has a
string with a rock tied to it. When the
car accelerates, he notices that the string with the rock makes an angle of 35
degrees with the vertical. How many
seconds does it take to go from 0 to 60 mph? Draw a figure, State the
principle, Solve the problem. 60 mph = ? m/s
(show how to convert)
There are several ways to
describe the principle on this problem. The
two forces acting on the rock (gravity + string) must produce a net force in
the horizontal direction.
35º mg
The acceleration is 6.86 m/s2
v = v0 + at so t = v/a
The time to attain 26.8 m/s
is 3.9 seconds.
What velocity must the space
shuttle have to stay in orbit 100 km above the earth’s surface? How much should the velocity change to move
100 m further out from the earth?
Draw a figure, State the principle, Solve the
problem
Principle: In order for the
space shuttle (ms) to stay in
orbit the force of gravity must supply the centripetal force:
To remain at a radius of
6,480,000 m, the velocity must be 7845.597 m/s
To remain at a radius of
6,480,100 m, the velocity must be 7845.537 m/s
The shuttle needs to slow down .06 m/s to move
100 m further from the Earth.
A 500 kg car is traveling
west at 30 m/s when struck by a drunken driver in a 1000 kg pickup traveling 50
m/s, 25 degrees north of east. The two
cars stick together after the collision. What is the velocity of the vehicles
after the collision? Is this collision
elastic or inelastic? How can you tell
for sure? Draw a figure, State the principle, Solve the problem
Final velocity of the truck
and car stuck together is 24.6 m/s at an
angle of 34.9 º.
Explain what would have
happened (and sketch the results) if the above collision would have been
elastic.
If the collision had been
elastic, the vehicles would have bounced off each other with no damage to
either and no loss of energy. The sum of
the momentum after the collision would have been the same as the above result.
A 200 g block of iron with a
temperature of 25ºC slides down a 30 degree incline that is 5 m long and has a
coefficient of friction of 0.2. How fast
is the block going when it reaches the bottom?
Assuming that all the heat energy goes into the iron block, what is the
temperature of the block at the bottom of the incline? Draw free body and net force diagrams, State
the principle, solve the problem.
Principle: The potential
energy of the block at the top of the incline is changed into K.E. and heat
energy (due to the friction).
5m
The height of the block at the beginning is 2.5m.
30° FN
P.E. = K.E. + friction work (work = force·distance)
mgh = ½ mv2+5m·
μFN = ½ mv2+ 5m·μmgcos30°
where FN = mg cos
30°
v2 = 49 – 17
v = 5.66 m/s
The velocity of the block at
the bottom of the incline is 5.66 m/s.
The energy lost to friction
is 5m·μmgcos30° = 1.7 joules = mcFeΔT
The temperature of the block
at the bottom of the incline (CFe = 450 j/kg-ºC)
so ΔT is 25.00188 ºC
After the block reaches the
level surface, the coefficient of friction remains the same. How far will the block slide before coming to
a stop? State the principle, solve the
problem.
Principle: The K.E. of the block at the bottom of the incline
will do work against friction.
½ mv2 = F·d where
the force is μmg.
The block will travel 8.17 m
before coming to a stop.
A bow has a 300 newton pull which is constant throughout the drawback of the arrow. How far would one draw back the string to shoot a 50 gram arrow 200 m straight up into the air? If the arrow were aluminum and were shot into a tree with the same drawback; assuming half the energy ended up in the arrow and that its original temperature was 20 Celsius, what would the final temperature of the arrow be?
The bow must be drawn back
32.6 cm to shoot the arrow 200 m high.
If the arrow is shot into the
tree and half the energy goes into the arrow, its temperature will be 21.09
ºC (The specific heat of aluminum is 900
j/(g -ºC)
The arrow in the above
problem is shot at an angle of 20 degrees with the vertical from the top a 50 m
building. How far will the arrow
go? Write the principle necessary to
solve the problem. Solve the problem.
Initial velocity of the arrow
is 62.6 m/s2
Time to top of path is 6
sec. Max height is 226 m. Total flight time is 12.79 s, the distance
traveled is 273.8 m.
A comet is traveling v0
when it is at its closest to the sun (3 x 107 km). How fast will it be going when it is at its furthest
point from the sun (1.5 x 1010 km)?
Write the principle. Solve the
problem.
Principle: The angular
momentum of the comet is the same at all times, including when it is close to
the sun and far form the sun.
mr1v1 =
mr2v2
v = 0.002 v0
A rifle fires a 100 gram
bullet with a temperature of 100º with a velocity of 100 m/s into 1.5 kg of
water that is also at 100º. How much of the water is changed to steam? Write the principle and solve the problem.
0.2216 grams of water will be
changed to steam.
A 100 g weight will stretch a
spring 15 cm. Write the equation of
motion for a 20 g weight placed on the spring and displaced 2 cm. Also find the frequency and the period of the
oscillations of the 20 g weight.
x = 2