Metric System Problem: 1.2.6 The diameter of an aluminum atom is about 0.24 nm, and the nuclear diameter

| October 22, 2018

Metric System
Problem: 1.2.6
The diameter of an aluminum atom is
about 0.24 nm, and the nuclear diameter is about 7.2 fm
(femtometer = 10−15 meter). (a) If the atom’s diameter
were expanded to the length of an American football field (91.44 m) and the
nuclear diameter expanded proportionally, what would be the nuclear diameter in
meters? (b) Is the saying that “the atom is mostly empty space” confirmed
by these figures?
(a) m
(b) Yes No

Problem: 1.8.2
Freefall acceleration g is
the acceleration due to gravity. It equals 9.80 meters per second squared near
the Earth’s surface. (a) What does it equal in feet per second squared? (b) In
miles per second squared? (c) In miles per hour squared?
(a) ft/s2
(b) mi/s2
(c) mi/h2

Problem: 1.8.4
You are on the phone with a friend
in Greece, who tells you that he has just caught a fish L cm long in the
Mediterranean Sea. Assuming he is telling the truth, what is the length of the
fish in inches?

Problem: 1.8.7
Mercury orbits the Sun at a mean
distance of 57,900,000 kilometers. (a) What is this distance in meters? Use
scientific notation to express your answer and state it with three significant
figures. (b) Pluto orbits at a mean distance of 5.91×1012 meters from the Sun. What is this distance in kilometers?
(a) m

In 2003, Bill Gates was worth 40.7
billion dollars. (a) Express this figure in dollars in scientific notation. (b)
Assume a dollar is worth 2,060 Italian lire. State Bill Gates’s net worth in
lire in scientific notation.
(a) dollars
(b) lire

Dimensional Analysis
Problem: 1.10.2
The dimensions for force are the
product of mass and length, divided by time squared. Newton’s law of
gravitation states that the gravitational force between two objects equals a
constant, G, times the product of the mass of each object, divided by
the square of the distance between them. What must the dimensions of the
constant be?


Problem: 1.10.4
The kinetic energy of an object is
given by the equation KE = (1/2)mv2, where m is mass and v is speed, with
dimensions L/T. What are the dimensions of KE?


Problem: 1.11.2
Evaluate (5.7×106 kg) × (6.3×10−2
m/s2) and express the answer in scientific notation.

Problem: 1.13.4
You have $1.14×104 in your checking account but must pay $3.30×103 in tuition. What is the balance in your checking account
after you pay your tuition? Express the answer in scientific notation.

Problem: 1.17.2
Suzy is holding her kite on a string
25.0 m long when the kite hits the top of a flagpole, which is f m
higher than her hands. Assuming that the string is taut and forms a straight
line, what is the horizontal distance from her hands to the flagpole?

Graphical Analysis of Motion
Problem: 2.C.8
Elaine wants to return a video she
rented at the video store, which is 5.0 kilometers away in the positive
direction. It takes her 10 minutes to drive to the store, 1.0 minute to deposit
the videotape, and 9.0 more minutes to drive home. What is her average velocity
for the entire trip?

Problem: 2.2.2
The school bus picks up Brian in
front of his house and takes him on a straight-line x km bus ride
to school in the positive direction. He walks home after school. If the front
of Brian’s house is the origin, (a) what is the position of the school, (b)
what is his displacement on the walk home, and (c) what is his displacement due
to the combination of the bus journey and his walk home?
(a) km
(b) km
(c) km

Problem: 2.3.2
A jogger is moving at a constant
velocity of +3.0 m/s directly towards a traffic light that is 100 meters
away. If the traffic light is at the origin, x = 0 m,
what is her position after running 20 seconds?

Problem: 2.4.4
You made a journey, and your displacement
was +95.0 km. Your initial velocity was +167 km/h and your final
velocity was −26.0 km/h. The journey took 43.0 minutes. What was your
average velocity in kilometers per hour?

Problem: 2.9.2
A graph of the velocity versus time
of a hockey puck is shown. Calculate the puck’s displacement from t = 1.0
s to t = 4.0 s.


Problem: 2.10.2
A sailboat is moving across the
water at 3.0 m/s. A gust of wind fills its sails and it accelerates at a
constant 2.0 m/s2. At the same instant, a motorboat
at rest starts its engines and accelerates at 4.0 m/s2. After 3.0 seconds have elapsed, find the velocity of (a)
the sailboat, and (b) the motorboat.
(a) m/s
(b) m/s

Problem: 2.11.5
The velocity versus time graph of an
ant is shown. What is the ant’s acceleration at (a) t = 1.0 s,
(b) t = 3.0 s, and (c) t = 5.0 s?

(a) cm/s2
(b) cm/s2
(c) cm/s2

Equation of Motion
Problem: 2.18.4
The brochure advertising a sports
car states that the car can be moving at 100.0 km/h, and stop in 37.19
meters. What is its average acceleration during a stop from that velocity?
Express your answer in m/s2. Consider the car’s initial
velocity to be a positive quantity.

Problem: 2.23.2
A watermelon cannon fires a
watermelon vertically up into the air at a velocity of +v m/s,
starting from an initial position 1.20 meters above the ground. When the
watermelon reaches the peak of its flight, what is (a) its velocity, (b) its
acceleration, (c) the elapsed time, and (d) its height above the ground?
(a) m/s
(b) m/s2
(c) s
(d) m

To determine freefall acceleration
on a moon with no atmosphere, you drop your handkerchief off the roof of a
baseball stadium there. The roof is 113 meters tall. The handkerchief reaches
the ground in 18.2 seconds. What is freefall acceleration on this moon? (State
the result as a positive quantity.)

Problem: 2.23.6
You are a bungee jumping fanatic and
want to be the first bungee jumper on Jupiter. The length of your bungee cord
is 45.0 m. Freefall acceleration on Jupiter is 23.1 m/s2. What is the ratio of your speed on Jupiter to your speed
on Earth when you have dropped 45.0 m? Ignore the effects of air
resistance and assume that you start at rest.

Problem: 2.23.8
You stand near the edge of Half Dome
in Yosemite, reach your arm over the railing, and (thoughtlessly, since what
goes up does come down and there are people below) throw a rock upward at 8.00
m/s. Half Dome is 1460 meters high. How long does it take for the rock to reach
the ground? Ignore air resistance.

Vector Addition
Problem: 3.C.7
A small crab fishing boat travels
from Colon City on the Pacific Ocean, through the Panama Canal, to Panama City
on the Atlantic Ocean. A large cruise ship travels from Colon City to Panama
City by sailing all the way around the Cape Horn at the southern tip of South
America. Do these two voyages have equal displacement vectors?
Yes No

Write the vectors labeled A, B
and C with rectangular coordinates.

(a) A = ( ,
(b) B = ( , )
(c) C = ( , )

Problem: 3.6.2
Solve for the unknown variables:
(a) (a, b) + (3, x) = (6, 7)
(b) (11, c) + (d, y) =(-12, −3)
(c) (5, 5) + (e, 4) = (2, f)
(d) (z, −3) − (5, g) = (h, 2)
(a) a = ; b
(b) c = ; d =
(c) e = ; f =
(d) g = ; h =

Addition of vectors
Find the component of each of
the following vectors (show your work):










For the diagram below, identify
the resultant (A, B, or C) and complete the table
(3 points):


is : __________________

Equation: _________________

of Resultant (find angle)______________

Given the vectors below, sketch
the following and draw the resultant (R). Do not draw a scaled vector diagram;
merely make a sketch. Label each vector. Clearly label the resultant (R).
(2 points)

Sketch for A + B + D (Clearly label
the Resultant)

B + C + E (Clearly label the Resultant)

For the following vector addition diagrams, add the components of each vector
and draw the resultant. Then, using the
Pythagorean Theorem, find the magnitude and direction (angle) of the
resultant. Show your work.
b) (3 points)
a) (3 points)

a) Sketch of resultant



(angle) __________

b) Sketch of resultant



Direction (angle) __________

c) (3 points)


(angle) _______________________

Motion in two dimensions
Problem: 4.C.2
Two girls decide to jump off a
diving board. Katherine steps off the diving board. Anna runs straight off the
diving board so that her initial velocity is solely horizontal. They both leave
the diving board at the same time. Which one lands in the water first?

Problem: 4.1.2
In a visit to the nation’s capital,
a foreign head of state travels from (−3.0, −4.0) km to
(4.0, 7.0) km. She then travels with a displacement of (−5.0, a) km.
Calculate the her total displacement over the course of the trip.
( , ) km

Problem: 4.1.4
An irresolute boater drives south at
28 km/h for a half hour, pauses for 5 minutes, and then drives east for 45
minutes at 32 km/h. State his displacement vector in kilometers using
rectangular coordinates. Use the convention that north and east are positive.
( , ) km

Problem: 4.2.1
A golf ball is launched at a 37.0°
angle from the horizontal at an initial velocity of 48.6 m/s. State its
initial velocity in rectangular coordinates.
( , ) m/s

Problem: 4.2.2
The displacement vector for a 15.0
second interval of a jet airplane’s flight is (x, −2430) m.
(a) What is the magnitude of the average velocity? (b) At what angle, measured
from the positive x axis, did the airplane fly during this time
interval? Express the angle as a number between −180° and +180°
(a) m/s
(b) °

Problem: 4.7.1
A friend throws a baseball
horizontally. He releases it at a height of 2.0 m and it lands 21 m
from his front foot, which is directly below the point at which he released the
baseball. (a) How long was it in the air? (b) How fast did he throw it?
(a) s
(b) m/s

Problem: 4.7.2
A cannon mounted on a pirate ship
fires a cannonball at 125 m/s horizontally, at a height of 17.5 m
above the ocean surface. Ignore air resistance. (a) How much time elapses until
it splashes into the water? (b) How far from the ship does it land?
(a) s
(b) m

Problem: 4.7.4
A juggler throws a ball with an
initial horizontal velocity of +1.1 m/s and an initial vertical velocity
of +5.7 m/s. What is its acceleration at the top of its flight path? Make
sure to consider the sign when responding. Consider the upward direction as

Interactive Problems

1. A clown in a circus is about to be
shot out of a cannon with a muzzle velocity of 15.2 m/s, aimed at 52.7° above
the horizontal. How far away should his fellow clowns position a net to ensure
that he lands unscathed? The net is at the same height as the mouth of the
Δx = m

2. A professional soccer player is 25.8
m from the goal, and kicks a hard shot from ground level. The ball hits the
crossbar on its way down, 2.44 m above the ground, 1.98 s after it was kicked.
What were the x and y components of the ball’s initial velocity? Take upward to
be the positive y direction.
vx = m/s

viy = m/s

Force and Newton’s Laws
Problem: 5.4.4
A dog on Earth weighs 136 N.
The same dog weighs 154 N on Neptune. What is the acceleration due to
gravity on Neptune?

Problem: 5.5.2
A 0.125 kg frozen hamburger
patty has two forces acting on it that determine its horizontal motion. A
2.30 N force pushes it to the left, and a 0.800 N force pushes it to
the right. (a) Taking right to be positive, what is the net force acting on it?
(b) What is its acceleration?
(a) N
(b) m/s2

The net force on a boat causes it to
accelerate at 1.55 m/s2. The mass of the boat is
215 kg. The same net force causes another boat to accelerate at
0.125 m/s2. (a) What is the mass of the second
boat? (b) One of the boats is now loaded on the other, and the same net force
is applied to this combined mass. What acceleration does it cause?
(a) kg
(b) m/s2

Problem: 5.11.4
A m kg box is resting on
a table. You push down on the box with a force of 8.00 N. What is the
magnitude of the normal force of the table on the block?

Problem: 5.12.2
During recess, Maria, who has mass
27.0 kg, hangs motionless on the monkey bars, with both hands gripping a
horizontal bar. Assume her arms are vertical and evenly support her body. What
is the tension in each of her arms?

Applications of Newton’s Laws
1. Use
the simulation in the interactive problem in Section 6.0 to answer the
following questions. (a) If F1 is
set to 12 N directly to the left, what should F2 be
set to so that the ball does not move when you press GO? (b) If F1 is
set to 10 N directly to the left, what should F2 be
set to so that the ball hits the target directly to the right of the ball? (c)
If F1 is set to 10 N straight up, what should F2 be
set to so that the ball hits the target that is up and to the right of the
(a) N,
(b) ,
(c) N,

2. A cat is stuck in a tree. You are designated with the job
to get it out, yet you do not want to climb the tree, because you may get stuck
as well. Instead you set up a pulley system. A rope (consider it massless) runs
from the seat you sit on over an ideal pulley and then to your hand. You pull
on the loose end of the rope with a force of 348 N. You weigh 612 N
and the seat you sit on weighs 16.0 N. (a) What is your acceleration? (b)
What force does the seat exert on you?
(a) m/s2

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