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MAKE-UP Test #4
1. (4 pts) You are standing at the edge of a cliff 20 m high, and you kick a soccer ball
horizontally with an initial speed of 20 m/s.
(a) How much time does it take for the ball to hit the ground?
Ans: 12 gt2 = 20 m ⇒ t2 = 2 × 20 m/(10 m/s2 ) ⇒ t = 2 s
(b) How far from the base of the cliff does the ball land?
Ans: 20 m/s × 2 s = 40 m
2. (2 pts) A new planet has been discovered that has twice the mass of the Earth and
has a radius twice the radius of the Earth. What is the acceleration of gravity (i.e. g)
on the surface of this new planet?
2
Ans: gEarth = GME /RE
, so for the new planet gnew = G(2ME )/(2RE )2 =
1
2
2
× (GME /RE ) = 5 m/s .
2
3. (4 pts) A block of mass 4 kg slides on a tabletop with no friction at a speed 3 m/s
until it bangs into and sticks to a second block of mass 2 kg which was initially at rest.
Together they continue to slide with a common speed vf .
(a) What is the common speed vf of the masses after the collision? Be certain to
include the appropriate units on your answer.
Ans: Use the conservation of momentum. pi = 4 kg × 3 m/s = pf = (4 kg +
2 kg)vf ⇒ vf = 2 m/s.
(b) How much kinetic energy was lost in the collision? Be certain to include the
appropriate units on your answer.
Ans: K.E.i = 21 × 4 kg × (3 m/s)2 = 18 J, and K.E.f =
so 6 J were lost in the collision.
1
1
2
× 6 kg × 4( m/s)2 = 12 J
4. (4 pts) A large, heavy rock has a mass of 90 kg and a density three times the density
of water. A rope is tied around the rock, and the rock is then lowered until it is 5 m
below the surface of the water.
(a) What is the weight (not mass! ) of an amount of water which has the same volume
as the rock?
Ans: Water has 1/3 the density of the rock, so the weight of the water is 1/3 the
weight of the rock, or (90 kg × 10 m/s2 )/3 = 300 N. This is also the buoyant force
acting on the rock.
(b) What is the tension in the rope? NOTE: Tension is a force, not a mass.
Ans: The buoyant force on the rock is the weight of the displaced water. The
buoyant force is 300 N so she tension in the rope is T = 900 N − 300 N = 600 N.
5. (2 pts) The ends of a 50 Volt battery are attached to two separate metal plates 1 cm
apart, each with an area of 10 cm2 . The two plates are parallel with one above the
other as shown in the diagram. A small ball bearing, about 1mm in diameter, has
1Coulomb of positive charge on it, and you are holding it very close to the negatively
charged metal plate.
(a) How much energy would you have to provide in order to move the ball bearing
to the positively charged plate?
Ans: 1 C × 50 V = 1000 J.
(b) Is this energy positive or negative?
Ans: Positive
6. (2 pts) A two meter long see-saw is balanced on a fulcrum in the middle. A girl of
mass 40 kg sits at one end of the see-saw. A boy of mass 50 kg sits on the other side
of the see-saw to balance the see-saw. How far is the boy from the fulcrum?
Ans: 0.8 m
2
7. (4 pts) You have three objects of identical mass and radius that will roll down an
inclined plane. Mass A is a uniform solid cylinder. Mass B is a hoop—all of the mass
is distributed along the outer rim of the object. Mass C is concentrated at the center
of the object with just very little mass going around the rim—this looks somewhat
like a bicycle wheel.
(a) If a race were held rolling all three objects down a ramp, which object would be
the first one down the ramp?
Ans: object C
(b) Which object would be last down the ramp?
Ans: object A
8. (2 pts) A spool with a pink ribbon around it is on the front desktop. If the ribbon is
pulled gently to the right, and if the spool rolls without slipping, it will
(Circle your answer.)
(a)
(b)
(c)
(d)
move to the left.
stay in the same place.
move to the right.
lift off the table.
9. (4 pts) At the front of the classroom is a large water-filled jar, on a turntable, with
an orange ball tied to a string that keeps it from floating to the top, and a blue ball
that is tied to a string that keeps it from sinking to the bottom. When the turntable
is spun ...
(a) Does the orange ball move out or in?
Ans: in
(b) Does the blue ball move out or in?
Ans: out
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TEST #3
1. (2 pts)
(a) If I hold a piece of paper at one end horizontally (as I did in class) and blow
across the top of the paper, will it
do nothing
or
lift up higher
or
droop further down?
(b) If I hold two pieces of paper vertically, close to each other, one in each hand and
blow between them will they
do nothing
or
move further apart
or
move closer together?
2. (1 pt) Two “plates” of an electroscope are charged and they both spread out as shown
in the diagram, and as seen on the desk. Circle the correct statement regarding the
two “plates.”
(a) Each plate has an electric charge of the same type, i.e. both plates are positive
or both plates are negative.
(b) Each plate has an electric charge of a different type, i.e. one plate is positive and
the other is negative.
3. (2 pts) Which has a lower temperature: A piece of metal pipe supporting your chair,
or the paper that this test is printed on?
Circle the correct answer:
Metal pipe,
The test,
They are the same temperature.
4. (4 pts) When water flows through a pipe as shown in the diagram, it flows most slowly
in region A, and most rapidly through region C.
(a) Which region has the greatest pressure?
Ans: A
(b) Which region has the least pressure?
Ans: C
5. (4 pts) Typical walking speed depends upon the length ` of your leg (which determines
how long each step is) and also upon the average time T p
that a single step takes, where
a pendulum of length ` has a natural period of T = 2π `/g.
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(a) Would you walk “faster” or “slower” if your legs were longer? Circle one of those
two choices.
Ans: faster
(b) If your natural walking speed is v0 , what would your natural walking speed be if
your legs were twice as long?
p
√
Ans: v ∼ `/T ∼ `/(2π `/g) ∼ g`/2π, so if your legs were twice√as long
(` → 2` in the previous formula) your walking speed would increase by 2.
6. (4 pts) A container is initially filled with a gas at 30 Atmospheres of pressure with a
temperature of 200◦ K. Some of the gas is then released until the pressure drops to 6
Atmospheres, but the temperature remains at 200◦ K.
(a) What fraction of the original amount of gas remains in the container?
Ans: 30/6 = 1/5
(b) The gas remaining in the container is then heated until the pressure in the container is again 30 Atmospheres. Now, what is the temperature of the gas in
◦
K?
Ans: P V = N kT , so if V , N and k do not change, but T does change, then it
needs to increase by a factor of 5 in order to raise P back to 30 Atmospheres.
So, T must be raised to 1000◦ K.
7. (2 pts) A large, heavy rock has a weight M g and a density twice the density of water.
What would a scale read if the rock and the scale were both submerged one meter
under the water in a swimming pool?
Ans: This was a poorly worded problem, and everyone was given 2 pts.
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8. (8 pts) Two organ pipes are each closed at one end and open at the other. Also, they
have differing lengths L1 and L2 = 2L1 as shown in the diagram. The “shape” of the
wave in each pipe is shown in the sketch below.
(a) Which pipe emits a sound wave with the longest wavelength? Pipe1 or Pipe2 ?
(b) Which pipe emits a sound wave with the highest frequency? Pipe1 or Pipe2 ?
(c) What is the frequency of the sound from Pipe1 ? Give your answer in terms of
L1 , and the speed of sound vs .
Ans: vs /4L
(d) If the frequency of the sound from Pipe1 is 330 cycles/s (or 330 Hz) then what is
the frequency of the sound from Pipe2 ?
Ans: f1 = vs /λ1 and f2 = vs /λ2 . From the diagrams and the wavelengths we see
that λ2 = λ1 /2. We know that the speed of sound is 330 m/s = vs = λ1 f1 = λ2 f2 ,
so if λ2 is twice as big as λ1 it must be that f2 is half the value of f1 , so the
answer is 165 Hz.
9. (2pts) The ends of a 100 Volt battery are attached to two separate metal plates, each
with an area of 1 m2 , and 0.1 m apart. The two plates are parallel with one above the
other as shown in the diagram. A small ball bearing has +10Coulombs of charge on
it and it starts very close to the positively charged metal plate. How much energy in
Joules does the ball bearing have when it hits the negatively charged plate?
Ans: 10 C × 100 V = 1000 J.
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TEST #2
1. (2 pts) An angle of 120◦ is equivalent to approximately how many radians? Give your
answer to at least 1 significant figure.
Ans: 360◦ = 2π ⇒ 120◦ = 2π/3 ≈ 2
2. (2 pts) An automobile with wheels of radius 0.1 m is traveling with a speed of 2 m/s.
What is the angular velocity of the wheel in units of radians/second?
Ans: v = ωR ⇒ ω = v/R = 20radians/sec
3. (2 pts) A two meter long see-saw is balanced in the middle. A girl of mass 30 kg sits
on one end, and a boy sits 0.5 m away from the other end. What is the mass of the
boy?
Ans: 60 kg
4. (2 pts) Imagine doing the following experiment: You stand in front of a foggy mirror
at a distance of the length of your arm. You then draw the outline of the image of
your face on the mirror. You next move backward doubling the distance between
you and the mirror. As you now view your image in the mirror, is the image inside
the original outline, outside the original outline, or the same size as the original outline?
(Circle your answer.)
(a) Inside
(b) Outside
(c) Same size
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5. (2 pts) A balance beam 1 m long has a fulcrum in the middle. A 3 kg mass hangs at
the far left hand end of the beam, and a 2 kg mass hangs at the far right hand end
of the beam. Where on the beam should you hang a second 2 kg mass so that the
arrangement of masses will balance. Give your answer as the distance as measured
from the left hand end of the beam.
Ans:
6. (6 pts) A hand grenade with a mass of 3 kg explodes into two pieces. One piece has a
mass of 1 kg and moves with a speed of 40 m/s.
(a) What is the mass of the second piece of the hand grenade?
Ans: 2 kg.
(b) How fast is the second piece moving after the explosion?
Ans: From the conservation of momentum, 20 m/s.
(c) Which of the two parts of the hand grenade has more kinetic energy after the
explosion?
Ans: The 1 kg mass.
7. (4 pts) A 5 kg block is held at the top of a frictionless slide inclined at 30◦ from the
horizontal. The top of the slide is 2 m above the ground. The length of the slide is
4 m. After the block is released, how fast will it be moving when it reaches the bottom
of the slide?
√
√
Ans: Use conservation of energy: P.E. = mgh = 12 mv 2 , so v = 2gh = 40 m/s.
8. (2 pts) A spool with a pink ribbon around it is on the front desktop. If the ribbon is
pulled gently to the right, and if the spool rolls without slipping, it will
(Circle your answer.)
(a)
(b)
(c)
(d)
move to the left.
stay in the same place.
move to the right.
lift off the table.
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9. (4 pts) A block of mass m slides with no friction at a speed vi until it bangs into
and sticks to a second block, also of mass m. Together they continue to slide with a
common speed vf .
(a) What is the speed vf of the masses after the collision? Give your answer in terms
of m and vi .
Ans: Use the conservation of momentum. mvi = 2mvf ⇒ vf = vi /2
(b) How much kinetic energy was lost in the collision? Give your answer only in
terms of m and vi , and specifically not in terms of vf .
Ans: K.E.i = 12 mvi2 and K.E.f = 12 (m + m)vf2 = 41 mvi2 = 12 K.E.i was lost.
10. (4 pts) You have three objects of identical mass and radius that will roll down an
inclined plane. Mass A is a uniform solid cylinder. Mass B is a hoop—all of the mass
is distributed along the rim of the object. Mass C is concentrated at the center of
the object with just very little mass going around the rim—this looks somewhat like
a bicycle wheel.
(a) If a race were held rolling all three objects down a ramp, which object would be
the first one down the ramp?
(b) Which object would be last down the ramp?
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TEST #1
1. (2 pts) What is (2 × 103 ) × (2 × 10−2 )? Give your answer in the usual decimal form,
without any powers of ten.
Ans: 40
2. (4 pts) First you walk south 3 meters, then you walk east 4 meters.
(a) What is the distance from where you started to where you stopped?
√
√
√
Ans: 42 + 32 = 16 + 9 = 25 = 5 m
(b) You were walking at a speed of 2 m/s, so how much time did it take for you to
travel along that path?
Ans: Actual distance walked is 3 m + 4 m = 7 m.
7 m/(2 m/s) = 3.5 s
At 2 m/s the time is
3. (2 pts) Your mass is 60 kg, and you are standing on the surface of the Earth. What is
the magnitude of the force of gravity acting upon you?
Ans: Fgrav = mg = 60 kg × 10 m/s2 = 600 N.
4. (4 pts) You tie a rope around a tree trunk and pull with a force of 200 N.
(a) What is the tension in the rope?
Ans: 200 N
(b) What is the magnitude of the force that the tree exerts on the rope?
Ans: 200 N
5. (2 pts) A 5 kg block is at rest on a table top. What is the magnitude of the sum of all
of the forces acting on the block? This is also called the “net force.”
Ans: The block is not accelerating, so the net force is zero.
6. (2 pts) Two children slide down a frictionless slide at a playground. One child has a
mass of 30 kg and slides down the slide in 3 s. The other child has a mass of 60 kg.
How much time will it take the second child to slide down the slide?
Ans: 3 s
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7. (2 pts) An object of mass 20 kg is acted upon by three forces. One force is 3 N to the
right, the second is 5 N to the left. The object moves with a constant speed of 4 m/s to
the right. What is the magnitude and the direction (left or right) of the third force?
Ans: 2 N to the right.
8. (2 pts) An airplane flies in a horizontal circle of radius R = 500 m with a constant
speed of v = 100 m/s. What is the magnitude of the acceleration of the airplane?
Ans: a = v 2 /R = (100 m/s)2 /(500 m) = (10000/500) m/s2 = 20 m/s2
9. (2 pts) A new planet orbiting Alpha Centauri (the star nearest to our Sun) has a mass
one half the mass of the Earth and has a radius one half the radius of the Earth. What
is the acceleration of gravity (i.e. g) on the surface of this new planet?
2
Ans: gEarth = GME /RE
, so for the new planet gnew = G(ME /2)/(RE /2)2 =
2
2 × (GME /RE
) = 20 m/s2 .
10. (6 pts) A block of mass M5 = 5 kg and a second block of mass M3 = 3 kg are attached
to each other by a string. The 3 kg block has a second string attached to it with a
tension of 16 N which accelerates the combination of blocks to the right, as shown in
the figure.
(a) What is the acceleration of the 3 kg block?
Ans: Use F = ma, or 16 N = (5 kg + 3 kg)a ⇒ a = 16 N/(8 kg) = 2 m/s2 .
(b) What is the acceleration of the 5 kg block?
Ans: The same as for the 3 kg block, 2 m/s2 .
(c) What is the tension in the string between the two masses?
Ans: T = M5 a = 5 kg × 2 m/s2 = 10 N
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